book.bib

@book{xie2015,
  title = {Dynamic Documents with {R} and knitr},
  author = {Yihui Xie},
  publisher = {Chapman and Hall/CRC},
  address = {Boca Raton, Florida},
  year = {2015},
  edition = {2nd},
  note = {ISBN 978-1498716963},
  url = {http://yihui.name/knitr/},
}

@inbook{lugo2007,
	author = {María Ana Lugo},
	year = {2007},
	title = {Comparing Multidimensional Indices of Inequality: methods and application},
	booktitle = {Inequality and Poverty},
	pages = {213-236},
	doi = {10.1016/S1049-2585(06)14010-7},
	URL = {http://www.emeraldinsight.com/doi/abs/10.1016/S1049-2585%2806%2914010-7},
	eprint = {http://www.emeraldinsight.com/doi/pdf/10.1016/S1049-2585%2806%2914010-7},
	abstract = { The paper examines several measures of multidimensional inequality, analysing their properties and majorisation criteria. Moreover, it presents a new measure which generalises Bourguignon (1999) and includes Tsui measures (1999), while preserving the advantages of Maasoumi's method (1986) of explicitly acknowledging the role of parameters relevant to multivariate settings. Finally, an application to Argentine data is provided in order to illustrate the decisions involved in the process of applying these measures and the usefulness of having appropriate criteria when making those decisions. }
}



@article {rohde2016,
	author = {Nicholas Rohde},
	title = {J-divergence measurements of economic inequality},
	journal = {Journal of the Royal Statistical Society: Series A (Statistics in Society)},
	volume = {179},
	number = {3},
	issn = {1467-985X},
	url = {http://dx.doi.org/10.1111/rssa.12153},
	doi = {10.1111/rssa.12153},
	pages = {847--870},
	keywords = {Distance, Divergence, Inequality, Information theory},
	year = {2016}
}


@article{alkire2011,
  author={Sabina Alkire and James Foster},
  title={Counting and multidimensional poverty measurement},
  journal={Journal of Public Economics},
  year={2011},
  volume={95},
  number={7-8},
  pages={476-487},
  month={August},
  keywords={ Multidimensional poverty measurement Capability approach Identification FGT measures Decomposabilit},
  abstract={This paper proposes a new methodology for multidimensional poverty measurement consisting of an identification method [rho]k that extends the traditional intersection and union approaches, and a class of poverty measures M[alpha]. Our identification step employs two forms of cutoff: one within each dimension to determine whether a person is deprived in that dimension, and a second across dimensions that identifies the poor by 'counting' the dimensions in which a person is deprived. The aggregation step employs the FGT measures, appropriately adjusted to account for multidimensionality. The axioms are presented as joint restrictions on identification and the measures, and the methodology satisfies a range of desirable properties including decomposability. The identification method is particularly well suited for use with ordinal data, as is the first of our measures, the adjusted headcount ratio M0. We present some dominance results and an interpretation of the adjusted headcount ratio as a measure of unfreedom. Examples from the US and Indonesia illustrate our methodology.},
  url={https://ideas.repec.org/a/eee/pubeco/v95y2011i7-8p476-487.html}
}


@misc{pacifico2016,
	title = {MPI: Stata module to compute the Alkire-Foster multidimensional poverty measures and their decomposition by deprivation indicators and population sub-groups},
	author = {Daniele Pacifico and Felix Poge},
	year = {2016},
	abstract = {MPI estimates the Adjusted Multidimensional Headcount Ratio developed by Alkire and Foster (2011), also known as the Multidimensional Poverty Index. With ordinal and real-valued indicators MPI allows estimating the entire parametric class of Alkire-Foster poverty measures for arbitrary values of the poverty-aversion parameter. All poverty measures can be conveniently decomposed by deprivation indicators and population sub-groups. Users can specify an indefinite number of indicators and use a flexible weighting structure for each of them. Poverty thresholds can be set directly within the command line using a flexible notation for identifying who is above or below the threshold. Deprivation indicators can be grouped into broader policy domains which simplifies the analysis of results in many empirical applications. The survey design is fully taken into account when computing indicators, standard errors and covariances. MPI allows using standard Stata features such as nonparametric bootstrap estimation of the results and mean-comparison tests.},
	keywords = {poverty; poverty index; Alkire; Foster},
	url = {http://EconPapers.repec.org/RePEc:boc:bocode:s458120}
}




@book{alkire2015,
  title = {Multidimensional Poverty Measurement and Analysis},
  author = {Sabina Alkire and James Foster and Suman Seth and Maria Emma Santos and Jose Manuel Roche and Paola Ballon},
  publisher = {Oxford University Press},
  year = {2015},
  note = {ISBN 9780199689491}
}


@article{foster1984,
 ISSN = {00129682, 14680262},
 URL = {http://www.jstor.org/stable/1913475},
 author = {James Foster and Joel Greer and Erik Thorbecke},
 journal = {Econometrica},
 number = {3},
 pages = {761-766},
 publisher = {Wiley, Econometric Society},
 title = {A Class of Decomposable Poverty Measures},
 volume = {52},
 year = {1984}
}


@article{berger2003,
	author = {Yves G. Berger and Chris J. Skinner},
	title = {Variance estimation for a low income proportion},
	journal = {Journal of the Royal Statistical Society: Series C (Applied Statistics)},
	volume = {52},
	number = {4},
	publisher = {Blackwell Publishing},
	issn = {1467-9876},
	url = {http://dx.doi.org/10.1111/1467-9876.00417},
	doi = {10.1111/1467-9876.00417},
	pages = {457--468},
	keywords = {Calibration, Complex sampling design, Linearization, Poverty, Quantile, Raking, Survey weight},
	year = {2003}
}

@phdthesis{langel2012,
	author = {Matti Langel},
	title = {Measuring inequality in finite population sampling},
	year = {2012},
	URL = {http://doc.rero.ch/record/29204}
}

@article{langel2011,
  doi = {10.1007/s00184-011-0369-1},
  url = {https://doi.org/10.1007/s00184-011-0369-1},
  year = {2012},
  month = 9,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {75},
  number = {8},
  pages = {1093--1110},
  author = {Matti Langel and Yves Till{\'{e}}},
  title = {Inference by linearization for Zenga's new inequality index: a comparison with the Gini index},
  journal = {Metrika}
}

@article{osier2009,
	title = {Variance estimation for complex indicators of poverty and inequality},
	author = {Guillaume Osier},
	journal = {Journal of the European Survey Research Association},
	volume = {3},
	number = {3},
	year = {2009},
	pages = {167--195},
	url = {http://ojs.ub.uni-konstanz.de/srm/article/view/369},
	ISSN = {1864--3361}
}

@article{demnati2004,
	title = {{Linearization Variance Estimators for Survey Data}},
	author = {Demnati, A. and Rao, J. N. K.},
	journal = {Survey Methodology},
	volume = {30},
	number = {1},
	year = {2004},
	pages = {17--26},
	url = {https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2004001/article/6991-eng.pdf}
}

@article{deville1999,
	title = {Variance estimation for complex statistics and estimators: linearization and residual techniques},
	author = {Jean-Claude Deville},
	journal = {Survey Methodology},
	volume = {25},
	number = {2},
	year = {1999},
	pages = {193--203},
	url = {http://www.statcan.gc.ca/pub/12-001-x/1999002/article/4882-eng.pdf}
}

@article{kovacevic1997,
	title = {Variance Estimation for Measures of Income Inequality and Polarization - The Estimating Equations Approach},
	author = {Milorad Kovacevic and David Binder},
	journal = {Journal of Official Statistics},
	volume = {13},
	number = {1},
	year = {1997},
	pages = {41--58},
	url = {http://www.jos.nu/Articles/abstract.asp?article=13141}
}

@article{lerman1989,
	title = {Improving the accuracy of estimates of Gini coefficients},
	author = {Robert Lerman and Shlomo Yitzhaki},
	year = {1989},
	journal = {Journal of Econometrics},
	volume = {42},
	number = {1},
	pages = {43-47},
	url = {http://EconPapers.repec.org/RePEc:eee:econom:v:42:y:1989:i:1:p:43-47}
}



@article{shorrocks1984,
	ISSN = {00129682, 14680262},
	URL = {http://www.jstor.org/stable/1913511},
	abstract = {This paper examines the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup. It is shown that such decomposable inequality measures must be monotonic transformations of additively decomposable indices. The general functional form of decomposable indices is derived without assuming that the measures are differentiable. The analysis is suitable for extension to the many other kinds of indices for which a similar relationship between the overall index value and subaggregates is desirable.},
	author = {Anthony F. Shorrocks},
	journal = {Econometrica},
	number = {6},
	pages = {1369-1385},
	publisher = {Wiley, Econometric Society},
	title = {Inequality Decomposition by Population Subgroups},
	volume = {52},
	year = {1984}
}


@techreport{biewen2003,
	title = {Estimation of Generalized Entropy and Atkinson Inequality Indices from Complex Survey Data},
	author = {Martin Biewen and Stephen Jenkins},
	year = {2003},
	institution = {DIW Berlin, German Institute for Economic Research},
	type = {Discussion Papers of DIW Berlin},
	number = {345},
	abstract = {Applying a method suggested by Woodruff (1971), we derive the sampling variances of Generalized Entropy and Atkinson inequality indices when estimated from complex survey data. It turns out that this method also greatly simplifies the calculations for the i.i.d. case when compared to previous derivations in the literature. Both cases are illustrated with examples from the German Socio-Economic Panel Study and the British Household Panel Survey.},
	keywords = {Inequality; Statistical Inference; Complex Surveys},
	url = {http://EconPapers.repec.org/RePEc:diw:diwwpp:dp345}
}


@article{arnold2012,
	title = {On the Amato inequality index},
	author = {Barry C. Arnold},
	year = {2012},
	journal = {Statistics and Probability Letters},
	volume = {82},
	number = {8},
	pages = {1504-1506},
	abstract = {Amato (1968) proposed using the length of the Lorenz curve as an index of inequality. The index has been little used, perhaps because of the perceived difficulty in analytically evaluating the value of the index in specific situations. A simple representation of the index as an expectation of a particular convex function is presented here.},
	keywords = {Lorenz curve; Convex function; Curve length; Discrete approximation;},
	url = {http://EconPapers.repec.org/RePEc:eee:stapro:v:82:y:2012:i:8:p:1504-1506}
}

@article{barabesi2016,
	author = {Lucio Barabesi and Giancarlo Diana and Pier Francesco Perri},
	title = {Linearization of inequality indices in the design-based framework},
	journal = {Statistics},
	volume = {50},
	number = {5},
	pages = {1161-1172},
	year = {2016},
	doi = {10.1080/02331888.2015.1135924},
	URL = {http://dx.doi.org/10.1080/02331888.2015.1135924},
	eprint = {http://dx.doi.org/10.1080/02331888.2015.1135924},
	abstract = {Linearization methods are customarily adopted in sampling surveys to obtain approximated variance formulae for estimators of statistical functionals under the design-based approach. In the present paper, following the Deville [Variance estimation for complex statistics and estimators: linearization and residual techniques. Surv Methodol. 1999;25:193–203] approach stemming from the concept of design-based influence function, we provide a general result for linearizing a large family of population functionals which includes many of the inequality measures considered in social, economic and statistical studies, such as the Gini, Amato, Zenga, Atkinson and Generalized Entropy indices. The feasibility of our theoretical results is assessed by some simulation studies involving real and artificial data.}
}

@article{polisicchio2011,
	author = {Marcella Polisicchio and Francesco Porro},
	title = {A comparison between Lorenz L(P) curve and Zenga I(P) curve},
	journal = {Statistica Applicata},
	volume = {21},
	number = {3-4},
	pages = {289-301},
	year = {2011},
	URL = {http://hdl.handle.net/10281/49428},
	abstract = {Zenga has defined a new inequality curve I(p) and a new inequality index I. The purpose of this article is to compare Zenga’s I(p) curve and the well-known Lorenz L(p) curve, remarking the differences and the similarities existing between these evaluation tools of inequality. The comparison is performed by an analysis of the features of the two curves. The analytical expressions of the two curves for some classical distribution models used in inequality analysis are also provided, focusing on the role of the distribution parameters as inequality indicators.}
}

@incollection{bourguignon1999,
  author = "François Bourguignon",
  title = "Comment to 'Multidimensioned Approaches to Welfare Analysis' by Maasoumi, E.",
  editor = "Jacques Silber",
  booktitle = "Handbook of income inequality measurement",
  publisher = "Kluwer Academic",
  address = "London",
  year = 1999,
  pages = "477-484",
  chapter = 15,
}


@article{zenga2007,
	author = {Michele Zenga},
	title = {Inequality curve and inequality index based on the ratios between lower and upper arithmetic means},
	journal = {Statistica e Applicazioni},
	volume = {1},
	number = {4},
	pages = {3-27},
	year = {2007}
}

@TechReport{cowell2009,
  author={Frank A. Cowell and Emmanuel Flachaire and Sanghamitra Bandyopadhyay},
  title={Goodness-of-Fit: An Economic Approach},
  year=2009,
  month=Aug,
  institution={University of Oxford, Department of Economics},
  type={Economics Series Working Papers},
  url={https://ideas.repec.org/p/oxf/wpaper/444.html},
  number={444},
  abstract={Specific functional forms are often used in economic models of distributions; goodness-of-fit measures are used to assess whether a functional form is appropriate in the light of real-world data. Standard approaches use a distance criterion based on the EDF, an aggregation of differences in observed and theoretical cumulative frequencies. However, an economic approach to the problem should involve a measure of the information loss from using a badly-fitting model. This would involve an aggregation of, for example, individual income discrepancies between model and data. We provide an axiomatisation of an approach and applications to illustrate its importance.},
  keywords={Goodness of fit; Discrepancy; Income distribution; Inequality measurement},
  doi={},
}

@article {shannon1948,
author = {Claude E. Shannon},
title = {A Mathematical Theory of Communication},
journal = {Bell System Technical Journal},
volume = {27},
number = {3},
publisher = {Blackwell Publishing Ltd},
issn = {1538-7305},
url = {http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x},
doi = {10.1002/j.1538-7305.1948.tb01338.x},
pages = {379--423},
year = {1948},
}

@article{atkinson1970,
  author={Anthony B. Atkinson},
  title={On the Measurement of Inequality},
  journal={Journal of Economic Theory},
  year=1970,
  volume={2},
  number={3},
  pages={244-263},
  month={September},
  url={https://ideas.repec.org/a/eee/jetheo/v2y1970i3p244-263.html}
}


@techreport{jenkins2006,
title = {Estimation and interpretation of measures of inequality, poverty, and social welfare using Stata},
author = {Stephen Jenkins},
year = {2008},
institution = {Stata Users Group},
type = {North American Stata Users' Group Meetings 2006},
abstract = {This presentation reviews methods for summarizing and comparing income distributions, together with the related literature about variance estimation for a range of summary measures. Although the focus is on income and the perspective is that of an economist, the methods have been widely applied to other variables, including health-related ones, and by researchers from many disciplines. Topics covered include the measurement of inequality, poverty, and social welfare, and distributional comparisons based on the dominance methods as well as summary indices. Illustrations are provided using a suite of public-domain Stata programs written by the author and collaborators (e.g., glcurve, ineqdeco, povdeco, sumdist, svyatk, svygei, svylorenz), together with built-in commands.},
url = {http://EconPapers.repec.org/RePEc:boc:asug06:16}
}

@TechReport{jann2016,
  author={Ben Jann},
  title={{Estimating Lorenz and concentration curves in Stata}},
  year=2016,
  month=Jan,
  institution={University of Bern, Department of Social Sciences},
  type={University of Bern Social Sciences Working Papers},
  url={https://ideas.repec.org/p/bss/wpaper/15.html},
  number={15},
  abstract={Lorenz and concentration curves are widely used tools in inequality research. In this paper I present a new Stata command called -lorenz- that estimates Lorenz and concentration curves from individual-level data and, optionally, displays the results in a graph. The -lorenz- command supports relative as well as generalized, absolute, unnormalized, or custom-normalized Lorenz or concentration curves, and provides tools for computing contrasts between different subpopulations or outcome variables. Variance estimation for complex samples is fully supported.},
  keywords={Stata; Lorenz curve; concentration curve; inequality; income distribution; wealth distribution; grap},
  doi={},
}

@TechReport{lima2013,
  author={Luis Cristovao Ferreira Lima},
  title={{The Persistent Inequality in the Great Brazilian Cities: The Case of Brasília}},
  year=2013,
  month=Sep,
  institution={University of Brasília},
  type={MPRA Papers},
  url={https://mpra.ub.uni-muenchen.de/50938/},
  number={50938},
}


@Misc{vardpoor,
	author = {Juris Breidaks and Martins Liberts and Santa Ivanova},
	year = {2016},
	title = {vardpoor: Estimation of indicators on social exclusion and poverty and its linearization, variance estimation},
	note = {R package version 0.8.0},
	organization = {CSB},
	address = {Riga, Latvia},
}

@article{bourguignon2003,
doi	= {10.1023/a:1023913831342},
title	= {The Measurement of Multidimensional Poverty},
author	= {François Bourguignon and Satya R. Chakravarty},
publisher	= {Springer US},
journal	= {The Journal of Economic Inequality},
issnp	= {1569-1721},
issne	= {1573-8701},
year	= {2003},
month	= {04},
volume	= {1},
issue	= {1},
page	= {25--49},
url =       {http://gen.lib.rus.ec/scimag/index.php?s=10.1023/a:1023913831342},
}

@TechReport{vega2009,
  author={Maria Casilda Lasso de la Vega and Ana Urrutia and Henar Diez},
  title={{The Bourguignon and Chakravarty multidimensional poverty family: A characterization}},
  year=2009,
  month=03 ,
  institution={ECINEQ, Society for the Study of Economic Inequality},
  type={Working Papers},
  url={https://ideas.repec.org/p/inq/inqwps/ecineq2009-109.html},
  number={109},
  abstract={The family of multidimensional poverty indices introduced by Bourguignon and Chakravarty (Journal of Economic Inequality, 2003) has attracted a great deal of interest in the field of poverty measurement. In this note we explore a number of properties fulfilled by the members of this family, related to both the way to aggregate, for each individual, the deprivations in the various attributes, and the procedure for combining the individuals' overall deprivations. Then we show that the properties we highlight characterize the functional form of the family.},
  keywords={multidimensional poverty indices; Bourguignon and Chakravarty family; deprivation.},
  doi={},
}

@BOOK{W85,
  title = {Introduction to Variance Estimation},
  publisher = {Springer-Verlag},
  year = {1985},
  author = {Wolter, K. M.},
  address = {New York}
}

@TechReport{cobham2015,
  author={Alex Cobham and Luke Schlogl and Andy Sumner},
  title={{Inequality and the Tails: The Palma Proposition and Ratio Revisited}},
  year={2015},
  month={07} ,
  institution={United Nations, Department of Economics and Social Affairs},
  type={Working Papers},
  url={http://www.un.org/esa/desa/papers/2015/wp143_2015.pdf},
  number={143}
}

@article{verma2011,
doi	= {10.1080/02664763.2010.515674},
title	= {Taylor linearization sampling errors and design effects for poverty measures and other complex statistics},
author	= {Vijay Verma and Gianni Betti},
publisher	= {Taylor and Francis Group},
journal	= {Journal of Applied Statistics},
issnp	= {0266-4763},
issne	= {1360-0532},
year	= {2011},
month	= {08},
volume	= {38},
issue	= {8},
page	= {1549--1576},
url =       {http://dx.doi.org/10.1080/02664763.2010.515674},
}

@article{clark1981,
doi	= {10.2307/2232600},
title	= {On Indices for the Measurement of Poverty},
author	= {Stephen Clark and Richard Hemming and David Ulph},
publisher	= {John Wiley and Sons},
journal	= {The Economic Journal},
issnp	= {0013-0133},
issne	= {1468-0297},
year	= {1981},
month	= {06},
volume = {91},
issue	= {362},
page	= {515--526},
url = {http://www.jstor.org/stable/2232600},
}

@article{atkinson1987,
doi	= {10.2307/1911028},
title	= {On the Measurement of Poverty},
author = {Anthony B. Atkinson},
publisher	= {John Wiley and Sons},
journal	= {Econometrica},
issnp	= {0012-9682},
issne	= {1468-0262},
year = {1987},
month	= {07},
volume = {55},
issue	= {4},
page = {749--764},
url = {http://www.jstor.org/stable/1911028},
}

@TechReport{watts1968,
author={Harold W. Watts},
title={An economic definition of poverty},
year={1968},
institution={Institute For Research on Poverty},
type={Discussion Papers},
number = {5},
url={https://www.irp.wisc.edu/publications/dps/pdfs/dp568.pdf},
}

@book{haughton2009,
title = {Handbook on Poverty and Inequality},
author = {Jonathan Haughton and Shahidur Khandker},
publisher = {World Bank Publications},
isbn = {0821376136,9780821376133},
year = {2009},
series = {World Bank Training Series},
url = {https://openknowledge.worldbank.org/bitstream/handle/10986/11985/9780821376133.pdf},
}

@article{murdoch1998,
title = "Poverty, economic growth, and average exit time",
journal = "Economics Letters ",
volume = "59",
number = "3",
pages = "385--390",
year = "1998",
note = "",
issn = "0165-1765",
doi = "10.1016/S0165-1765(98)00070-6",
url = "http://www.sciencedirect.com/science/article/pii/S0165176598000706",
author = "Jonathan Morduch",
keywords = "Poverty measurement",
keywords = "Economic growth",
keywords = "Watts poverty measure",
keywords = "Bolivia",
keywords = "Bangladesh ",
abstract = "A simple transformation of the Watts poverty index yields a “meaningful” measure with appealing ordinal properties and a natural interpretation in terms of the potential for economic growth to alleviate poverty. The index is illustrated with data from Bangladesh and Bolivia. "
}

@article {aristondo2010,
author = {Aristondo, Oihana and De La Vega, Casilda Lasso and Urrutia, Ana},
title = {A new multiplicative decomposition for the Foster–Greer–Thorbecke poverty indices},
journal = {Bulletin of Economic Research},
volume = {62},
number = {3},
publisher = {Blackwell Publishing Ltd},
issn = {1467-8586},
url = {http://dx.doi.org/10.1111/j.1467-8586.2009.00320.x},
doi = {10.1111/j.1467-8586.2009.00320.x},
pages = {259--267},
keywords = {Foster–Greer–Thorbecke poverty indices, multiplicative decomposition, poverty measurement, I30, I32, D63},
year = {2010},
}

@article{chakravarty2008,
doi	= {10.1016/j.worlddev.2007.10.003},
title	= {On the Watts multidimensional poverty index and its decomposition},
author = {Satya R. Chakravarty and Joseph Deutsch and Jacques Silber},
publisher	= {Elsevier Science},
journal	= {World Development},
issnp	= {0305-750X},
year = {2008},
volume = {36},
issue	= {6},
page	= {1067--1077},
url = {http://dx.doi.org/10.1016/j.worlddev.2007.10.003},
}

@article{blackburn1989,
author = {McKinley L. Blackburn},
title = {Poverty measurement: an index related to a Theil measure of inequality},
journal = {Journal of Business \& Economic Statistics},
volume = {7},
number = {4},
pages = {475-481},
year = {1989},
doi = {10.1080/07350015.1989.10509760},
URL = {http://amstat.tandfonline.com/doi/abs/10.1080/07350015.1989.10509760},
eprint = {http://amstat.tandfonline.com/doi/pdf/10.1080/07350015.1989.10509760}
}

@book{ravallion2016,
  title = {The economics of poverty: history, measurement and policy},
  author = {Martin Ravallion},
  publisher = {Oxford University Press},
  address = {New York, USA},
  year = {2016},
  edition = {1st},
  note = {ISBN 10:0190212764, 13:9780190212766},
}

@book{deaton1997,
   title =     {The analysis of household surveys: a microeconomic approach to development policy},
   author =    {Angus Deaton},
   publisher = {World Bank Publications},
   isbn =      {0801852544,9780801852541,9780585237879},
   year =      {1997},
   }

@article{deaton2003,
doi	= {10.1080/0953531032000091144},
title	= {Household surveys, consumption, and the measurement of poverty},
author	= {Angus Deaton},
publisher	= {Taylor and Francis Group},
journal	= {Economic Systems Research},
issnp	= {0953-5314},
issne	= {1469-5758},
year	= {2003},
month	= {06},
volume	= {15},
issue	= {2},
page	= {135--159},
}

@article{bhat2007,
doi	= {10.1016/j.jeconom.2005.09.003},
title	= {Inference on inequality from household survey data},
author	= {Debopam Bhattacharya},
publisher	= {Elsevier Science},
journal	= {Journal of Econometrics},
issnp	= {0304-4076},
year	= {2007},
volume	= {137},
issue	= {2},
page	= {674--707},
}

@book{bedi2007,
   title =     {More than a pretty picture: using poverty maps to design better policies and interventions},
   author =    {Tara Bedi and Aline Coudouel and Kenneth Simler},
   publisher = {World Bank Publications},
   isbn =      {0821369318,9780821369319,9780821369326},
   year =      {2007},
   series =    {},
   edition =   {},
   volume =    {},
   }

@article{elbers2003,
  doi	= {10.1111/1468-0262.00399},
  title	= {Micro–Level Estimation of Poverty and Inequality},
  author	= {Chris Elbers and Jean O. Lanjouw and Peter Lanjouw},
  publisher	= {John Wiley and Sons},
  journal	= {Econometrica},
  issnp	= {0012-9682},
  issne	= {1468-0262},
  year	= {2003},
  volume	= {71},
  issue	= {1},
  page	= {355--364},
}

@article{dalton1920,
doi	= {10.2307/2223525},
title	= {The Measurement of the Inequality of Incomes},
author	= {Dalton, Hugh},
publisher	= {John Wiley & Sons},
journal	= {The Economic Journal},
issnp	= {0013-0133},
issne	= {1468-0297},
year	= {1920},
month	= {09},
volume	= {30},
issue	= {119},
page	= {348--361},
url =       {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/2223525},
}

@incollection{kramer1998,
   author =    {Walter Krämer},
   title =     {Measurement of Inequality},
   pages =     {39-62},
   booktitle = {Handbook of Applied Economic Statistics},
   editor =    {Amman Ullah and David E. A. Giles},
   publisher = {Marcel Dekker},
   address =   {New York},
   isbn =      {9781584883203,1584883200},
   year =      {1998},
   series =    {Statistics: A Series of Textbooks and Monographs},
   number =    {155},
   edition =   {1},
}

@article{mosler1994,
title = "Majorization in economic disparity measures",
journal = "Linear Algebra and its Applications",
volume = "199",
pages = "91 - 114",
year = "1994",
note = "Special Issue Honoring Ingram Olkin",
issn = "0024-3795",
doi = "https://doi.org/10.1016/0024-3795(94)90343-3",
url = "http://www.sciencedirect.com/science/article/pii/0024379594903433",
author = "Karl Mosler",
abstract = "Abstract This survey presents an account of univariate and multivariate majorization orderings and their characterization by various classes of economic disparity indices. First, a concise treatment of classical univariate results is given, including majorization with different means and different population sizes, as well as Lorenz orderings of relative and absolute disparity. Second, alternatives to the Pigou-Dalton principle of transfers are discussed which are based on transfers about a given threshold. Third, disparity in several attributes and multivariate majorization are investigated, and a multivariate version of the Lorenz curved is introduced."
}

@book{hardy1934,
   title =     {Inequalities},
   author =    {G. H. Hardy and J. E. Littlewood and G. Pólya},
   publisher = {Cambridge University Press},
   isbn =      {0521358809,9780521358804},
   year =      {1934},
   series =    {},
   edition =   {2},
   volume =    {},
}

@book{olkin2011,
   title =     {Inequalities: Theory of Majorization and Its Applications },
   author =    {Albert W. Marshall and Ingram Olkin and Barry C. Arnold},
   publisher = {Springer},
   isbn =      {9780387400877,9780387682761,0387400877},
   year =      {2011},
   series =    {Springer Series in Statistics},
   edition =   {2},
   volume =    {},
}

@book{fleur1996,
   title =     {Théories économiques de la Justice},
   author =    {Marc Fleurbaey},
   publisher = {Economica},
   year =      {1996},
   series =    {Économie et Statistiques Avancées},
   address =    {Paris}
}

@book{cowell2011,
   title =     {Measuring inequality},
   author =    {Cowell, Frank Alan},
   publisher = {Oxford University Press},
   isbn =      {978-0-19-959403-0,0199594031},
   year =      {2011},
   series =    {London School of Economics Perspectives in Economic Analysis},
   edition =   {3},
   address =   {New York},
}

@Article{medeiros2006,
  author   = {Medeiros, Marcelo},
  title    = {{The Rich and the Poor: The Construction of an Affluence Line from the Poverty Line}},
  doi      = {10.1007/s11205-005-7156-1},
  issn     = {1573-0921},
  number   = {1},
  pages    = {1--18},
  url      = {https://doi.org/10.1007/s11205-005-7156-1},
  volume   = {78},
  abstract = {The paper proposes a simple methodology to estimate an affluence line that depends on the knowledge of the income distribution and the poverty line for a given population. The idea that poverty is morally unacceptable and can be eradicated through redistribution of wealth provides the grounds for the methodology. The line is defined as the value that delimitates the aggregated income required to eradicate poverty by the way of transfers from the rich to the poor. I estimate an affluence line using Brazilian 1999 National Household Survey data and briefly discuss the results.},
  journal  = {Social Indicators Research},
  year     = {2006},
}

@article{brz2014,
author = {Michal Brzezinski},
title = {Statistical inference for richness measures},
journal = {Applied Economics},
volume = {46},
number = {14},
pages = {1599-1608},
year  = {2014},
publisher = {Routledge},
doi = {10.1080/00036846.2014.880106},
URL = {https://doi.org/10.1080/00036846.2014.880106},
eprint = {https://doi.org/10.1080/00036846.2014.880106},
    abstract = { Richness indices are distributional statistics used to measure the incomes, earnings or wealth of the rich. This article uses a linearization method to derive the sampling variances for recently introduced distributionally sensitive richness measures when estimated from survey data. The results are derived for two cases: (1) when the richness line is known and (2) when it has to be estimated from the sample. The proposed approach enables easy consideration of the effects of a complex sampling design. Monte Carlo results suggest that the proposed approach allows for reliable inference in case of ‘concave’ richness indices, but that it is not satisfactory in case of ‘convex’ richness measures. The standard bootstrap methods give similar results for ‘concave’ measures, but they are also unreliable for ‘convex’ indices. The performance of the bootstrap inference can be improved in some cases using a semi-parametric approach. The variance formulae are illustrated with a comparison of wealth richness in Canada, Sweden, the United Kingdom and the United States. }
}

@article{peichl2010,
author = {Peichl, Andreas and Schaefer, Thilo and Scheicher, Christoph},
title = {{Measuring Richness and Poverty: A micro data application to Europe and Germany}},
journal = {Review of Income and Wealth},
volume = {56},
number = {3},
pages = {597-619},
doi = {https://doi.org/10.1111/j.1475-4991.2010.00404.x},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1475-4991.2010.00404.x},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1475-4991.2010.00404.x},
abstract = {In this paper, we define a new class of richness measures. In contrast to the often used headcount, these new measures are sensitive to changes in rich individuals' incomes and, therefore, allow for a more sophisticated analysis of richness. We demonstrate the application of these new measures in analyzing the development of poverty and richness over time in Germany. Moreover, we compare Germany to many other European countries and investigate the impact of tax reforms on poverty and richness. Using these examples, we show the importance of taking the intensity of changes into account and not only the number of people beyond a given richness line (headcount). We propose to use the new measures in addition to the headcount index for a more comprehensive analysis of richness.},
year = {2010}
}


@article{molina2010,
author = {Molina, Isabel and Rao, J. N. K.},
title = {Small area estimation of poverty indicators},
journal = {Canadian Journal of Statistics},
volume = {38},
number = {3},
pages = {369-385},
keywords = {Empirical best estimator, Parametric bootstrap, Poverty mapping, MSC 2000: Primary 62D05, secondary 62G09},
doi = {https://doi.org/10.1002/cjs.10051},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cjs.10051},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cjs.10051},
abstract = {Abstract The authors propose to estimate nonlinear small area population parameters by using the empirical Bayes (best) method, based on a nested error model. They focus on poverty indicators as particular nonlinear parameters of interest, but the proposed methodology is applicable to general nonlinear parameters. They use a parametric bootstrap method to estimate the mean squared error of the empirical best estimators. They also study small sample properties of these estimators by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct area-specific estimators and other estimators obtained by “simulated” censuses. The authors also apply the proposed method to estimate poverty incidences and poverty gaps in Spanish provinces by gender with mean squared errors estimated by the mentioned parametric bootstrap method. For the Spanish data, results show a significant reduction in coefficient of variation of the proposed empirical best estimators over direct estimators for practically all domains. The Canadian Journal of Statistics 38: 369–385; 2010 © 2010 Statistical Society of Canada},
year = {2010}
}

@Article{cillia2021,
  author       = {Gussenbauer, Johannes and de Cillia, Gregor},
  journaltitle = {Statistical Journal of the IAOS},
  title        = {{The R-package \textit{surveysd}: Estimating standard errors for complex surveys with a rotating panel design}},
  doi          = {10.3233/SJI-200709},
  issn         = {1875-9254},
  number       = {1},
  pages        = {115--121},
  url          = {https://content.iospress.com/articles/statistical-journal-of-the-iaos/sji200709},
  volume       = {37},
  abstract     = {Surveys with a rotating panel design are a prominent tool for producing more efficient estimates for indicators regarding trends or net changes over time. Variance estimation for net changes becomes however more complicated due to a possibly high correlation between the panel waves. Therefore, these estimates are quite burdensome to produce with traditional means. With the R-package surveysd, we present a tool which supports a straightforward way for producing estimates and corresponding standard errors for complex surveys with a rotating panel design. The package uses bootstrap techniques which incorporate the panel design and thus makes it easy to estimate standard errors. In addition the package supports a method for producing more efficient estimates by cumulating multiple consecutive sample waves. This method can lead to a significant decrease in variance assuming that structural patterns for the indicator in question remain fairly robust over time. The usability of the package and variance improvement, using this bootstrap methodology, is demonstrated on data from the user database (UDB) for the EU Statistics on Income and Living Conditions of selected countries with various sampling designs},
  keywords     = {Complex surveys, variance estimation, bootstrapping, resampling, R-programming},
  month        = {3},
  year         = {2021},
}