On the Influence Function of the Quintile Share Ratio

Kpanzou, Tchilabalo Abozou

doi:10.1080/03610918.2013.788707

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…Cowell and Flachaire, 2007). Semi-parametric estimators have been developed and shown to be less sensitive to contaminations (see Kpanzou, 2011, Kpanzou et al;2013).…”

Section: Discussionmentioning

confidence: 99%

“…The Gini index has been studied extensively and its properties documented in a number of papers (see e.g. the survey papers Xu, 2004 and Langel and Tillé;2013). Indices, most notably the Zenga index, have recently been explored from various points of view; for example finite and asymptotic variance cases have been considered in Greselin et al (2009Greselin et al ( ), (2010, (2013) and (2014).…”

Section: Introductionmentioning

confidence: 99%

“…As is to be expected from its definition, the influence function of the QSR is unbounded. The form of its influence function has recently been derived by Kpanzou (2013). In Hulliger and Schoch (2009) robust estimators for the QSR are developed in order to decrease the sensitivity to outlying observations.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic distribution of the quintile share ratio estimator

Kpanzou¹

2014

jas

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Abstract. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators which cover four important dimensions of social inclusion (financial poverty, employment, health and education). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. From the definition of the QSR, a (traditional) nonparametric estimator for it follows easily as a plug-in-type estimator. However, not much is known about the theoretical properties of this estimator. In this paper the estimator is defined and its asymptotic distribution theory derived. Using a simulation study, some finite sample properties of the limiting normal distribution are explored and reported on.Résumé. Le rapport des quintiles (QSR) est une mesure d'inégalité introduite récemment et fait partie des indicateurs européens couvrant quatre dimensions importantes de l'inclusion sociale,à savoir, la pauvreté, l'emploi, la santé et l'éducation. En 2001, le Conseil Européen a décidé que l'inégalité du revenu dans les pays membres de l'Union Européenne devrait etre décrite par un certain nombre d'indicateurs y compris le QSR. De part sa définition, on obtient facilement un estimateur de substitution pour cette mesure d'inégalité. Cependant, très peu est connu sur les propriétés théoriques dudit estimateur. Dans cet article nous définissons l'estimateur nonparamétrique du QSR et nous donnons sa distribution limite. A travers des simulations, nous explorons la loi limite ainsi obtenue,à savoir la loi normale.

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“…Cowell and Flachaire, 2007). Semi-parametric estimators have been developed and shown to be less sensitive to contaminations (see Kpanzou, 2011, Kpanzou et al;2013).…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic distribution of the quintile share ratio estimator

Kpanzou¹

2014

jas

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“…where 1 A is an indicator function of a set A, is associated with the IF described below (see [16]). Let…”

Section: Appendix: a List Of Some Ifsmentioning

confidence: 99%

On the Influence Function for the Theil-Like Class of Inequality Measures

Kpanzou¹,

Ba²,

Mergane³

et al. 2019

JSTA

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On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986 1000. On the other hand, the influence function (IF) of statistics is an important tool in the asymptotics of a nonparametric statistic. This function has been and is being determined and analyzed in various aspects for a large number of statistics. We proceed to a unifying study of the IF of all the members of the so-called Theil-like family and regroup those IF's in one formula. Comparative studies become easier.

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“…As is to be expected from its definition, the influence function of the QSR is unbounded. The form of that influence function has been also derived by [30]. Also, [29] derived the asymptotic distribution of a non-parametric plug-in estimator for the QSR index.…”

Section: Introductionmentioning

confidence: 99%

Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions

Modou Kebe,

Deme,

Tchilabalo Abozou Kpanzou

et al. 2023

Eur. J. Pure Appl. Math.

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Evidence from micro-data shows that capital incomes are exceedingly volatile, which makes up a disproportionately high contribution to the overall inequality in populations with the heavy-tailed nature on the income distributions for many countries. The quintile share ratio (QSR) is a recently introduced measure of income inequality, also forming part of the European Laeken indicators and which cover four important dimensions of social inclusion (health, education, employment and financial poverty). In 2001, the European Council decided that income inequality in the European Union member states should be described using a number of indicators including the QSR. Non-parametric estimation has been developed on the QSR index for heavy-tailed capital incomes distributions. However, this method of estimation does not give satisfactory statistical performances, since it suffers badly from under coverage, and so we cannot rely on the non-parametric estimator. Hence, we need another estimator in the case of heavy tailed populations. This is the reason why we introduce, in this paper, a class of semi-parametric estimators of theQSR index of economic inequality for heavy-tailed income distributions. Our methodology is basedon the extreme value theory, which offers adequate statistical results for such distributions. Weestablish their asymptotic distribution, and through a simulation study, we illustrate their behaviorin terms of the absolute bias and the median squared error. The simulation results clearly showthat our estimators work well.

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On the Influence Function of the Quintile Share Ratio

Cited by 4 publications

References 10 publications

Asymptotic distribution of the quintile share ratio estimator

Asymptotic distribution of the quintile share ratio estimator

On the Influence Function for the Theil-Like Class of Inequality Measures

Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions

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