Unbiased estimation of the Gini coefficient

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-02-15 DOI:10.1016/j.spl.2025.110376

Banu Baydil, Victor H. de la Peña, Haolin Zou, Heyuan Yao

{"title":"Unbiased estimation of the Gini coefficient","authors":"Banu Baydil, Victor H. de la Peña, Haolin Zou, Heyuan Yao","doi":"10.1016/j.spl.2025.110376","DOIUrl":null,"url":null,"abstract":"<div><div>The Gini coefficient is a fundamental statistical measure of dispersion used widely across multiple fields. The interest in the study of the properties of the Gini coefficient is highlighted by the fact that every year the World Bank ranks the level of income inequality between countries using it. In order to calculate the coefficient, it is common practice to assume a Gamma-distributed set of values when modeling the dispersion of individual incomes in a given population. The asymptotic behavior of the sample Gini coefficient for populations following a Gamma distribution has been well-documented in the literature. However, research on the finite sample behavior has been absent due to the challenge posed by the denominator. This study aims to fill this gap by demonstrating theoretically that the sample Gini coefficient is an unbiased estimator of the population Gini coefficient for a population having Gamma (<span><math><mi>α</mi></math></span>, <span><math><mi>β</mi></math></span>) distribution. Furthermore, our result provides a way to quantify the downward bias due to grouping when the population Gini coefficient is estimated using the sample Gini coefficient of equal-sized groups.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110376"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715225000215","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

Abstract

The Gini coefficient is a fundamental statistical measure of dispersion used widely across multiple fields. The interest in the study of the properties of the Gini coefficient is highlighted by the fact that every year the World Bank ranks the level of income inequality between countries using it. In order to calculate the coefficient, it is common practice to assume a Gamma-distributed set of values when modeling the dispersion of individual incomes in a given population. The asymptotic behavior of the sample Gini coefficient for populations following a Gamma distribution has been well-documented in the literature. However, research on the finite sample behavior has been absent due to the challenge posed by the denominator. This study aims to fill this gap by demonstrating theoretically that the sample Gini coefficient is an unbiased estimator of the population Gini coefficient for a population having Gamma (

α

β

) distribution. Furthermore, our result provides a way to quantify the downward bias due to grouping when the population Gini coefficient is estimated using the sample Gini coefficient of equal-sized groups.

查看原文本刊更多论文

无偏估计基尼系数

基尼系数是一种基本的分散统计量度，在多个领域被广泛使用。世界银行每年都会使用基尼系数对国家间的收入不平等程度进行排名，这凸显了人们对基尼系数特性研究的兴趣。为了计算基尼系数，通常的做法是在给定人群中建立个人收入分散模型时，假设一组数值呈伽马分布。文献中对遵循伽马分布的人群的样本基尼系数的渐近行为已有详细记载。然而，由于分母带来的挑战，关于有限样本行为的研究一直缺失。本研究旨在填补这一空白，从理论上证明了对于具有伽马（α，β）分布的人口，样本基尼系数是人口基尼系数的无偏估计值。此外，我们的结果还提供了一种方法，当使用等规模群体的样本基尼系数估算总体基尼系数时，可以量化因群体分组而产生的向下偏差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.