Estimating the Gini index for heavy-tailed income distributions

2021 ◽  
Vol 55 (1) ◽  
pp. 15-28
Author(s):  
Amina Bari ◽  
Abdelaziz Rassoul ◽  
Hamid Ould Rouis
Keyword(s):  
Asymptotic Distribution ◽  
Simulation Study ◽  
Gini Index ◽  
Confidence Bounds ◽  
Income Distributions ◽  
Semiparametric Estimator ◽  
Heavy Tailed

In the present paper, we define and study one of the most popular indices which measures the inequality of capital incomes, known as the Gini index. We construct a semiparametric estimator for the Gini index in case of heavy-tailed income distributions and we establish its asymptotic distribution and derive bounds of confidence. We explore the performance of the confidence bounds in a simulation study and draw conclusions about capital incomes in some income distributions.

scholarly journals POT-Based Estimation of the Renewal Function of Interoccurrence Times of Heavy-Tailed Risks

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Abdelhakim Necir ◽  
Abdelaziz Rassoul ◽  
Djamel Meraghni
Keyword(s):  
Simulation Study ◽  
Estimation Method ◽  
Infinite Variance ◽  
Finite Sample ◽  
Renewal Function ◽  
Peaks Over Threshold ◽  
Confidence Bounds ◽  
Asymptotically Normal ◽  
Semiparametric Estimator ◽  
Heavy Tailed

Making use of the peaks over threshold (POT) estimation method, we propose a semiparametric estimator for the renewal function of interoccurrence times of heavy-tailed insurance claims with infinite variance. We prove that the proposed estimator is consistent and asymptotically normal, and we carry out a simulation study to compare its finite-sample behavior with respect to the nonparametric one. Our results provide actuaries with confidence bounds for the renewal function of dangerous risks.

An Alternative to Cohen's κ

2006 ◽  
Vol 11 (1) ◽  
pp. 12-24 ◽  
Author(s):  
Alexander von Eye
Keyword(s):  
Simulation Study ◽  
Null Hypothesis ◽  
Categorical Variables ◽  
Alternative Measure ◽  
Rater Agreement ◽  
Verbal Processing ◽  
Heavy Tailed ◽  
Applicant Selection

At the level of manifest categorical variables, a large number of coefficients and models for the examination of rater agreement has been proposed and used. The most popular of these is Cohen's κ. In this article, a new coefficient, κ s , is proposed as an alternative measure of rater agreement. Both κ and κ s allow researchers to determine whether agreement in groups of two or more raters is significantly beyond chance. Stouffer's z is used to test the null hypothesis that κ s = 0. The coefficient κ s allows one, in addition to evaluating rater agreement in a fashion parallel to κ, to (1) examine subsets of cells in agreement tables, (2) examine cells that indicate disagreement, (3) consider alternative chance models, (4) take covariates into account, and (5) compare independent samples. Results from a simulation study are reported, which suggest that (a) the four measures of rater agreement, Cohen's κ, Brennan and Prediger's κ n , raw agreement, and κ s are sensitive to the same data characteristics when evaluating rater agreement and (b) both the z-statistic for Cohen's κ and Stouffer's z for κ s are unimodally and symmetrically distributed, but slightly heavy-tailed. Examples use data from verbal processing and applicant selection.

scholarly journals A comparative study of the Gini coefficient estimators based on the linearization and U-statistics Methods

2017 ◽  
Vol 40 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Shahryar Mirzaei ◽  
Gholam Reza Mohtashami Borzadaran ◽  
Mohammad Amini
Keyword(s):  
Comparative Study ◽  
Simulation Study ◽  
Gini Coefficient ◽  
Gini Index ◽  
Real Data ◽  
Linearization Method ◽  
U Statistics ◽  
The Gini Coefficient

In this paper, we consider two well-known methods for analysis of the Gini index, which are U-statistics and linearization for some incomedistributions. In addition, we evaluate two different methods for some properties of their proposed estimators. Also, we compare two methods with resampling techniques in approximating some properties of the Gini index. A simulation study shows that the linearization method performs 'well' compared to the Gini estimator based on U-statistics. A brief study on real data supports our findings.

scholarly journals Log-Transform Kernel Density Estimation of Income Distribution

2016 ◽  
Vol 91 (1-2) ◽  
pp. 141-159 ◽  
Author(s):  
Arthur Charpentier ◽  
Emmanuel Flachaire
Keyword(s):  
Income Distribution ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Estimation Methods ◽  
Density Functions ◽  
Income Distributions ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Positive Support

Standard kernel density estimation methods are very often used in practice to estimate density functions. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. In this paper, we show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the density estimation.

scholarly journals A SIMPLE EFFICIENT INSTRUMENTAL VARIABLE ESTIMATOR FOR PANEL AR(p) MODELS WHEN BOTHNANDTARE LARGE

2009 ◽  
Vol 25 (3) ◽  
pp. 873-890 ◽  
Author(s):  
Kazuhiko Hayakawa
Keyword(s):  
Time Series ◽  
Lower Bound ◽  
Asymptotic Distribution ◽  
Cross Section ◽  
Simulation Study ◽  
Instrumental Variable ◽  
Asymptotic Variance ◽  
The Cross ◽  
Instrumental Variable Estimator ◽  
Normally Distributed

In this paper, we show that for panel AR(p) models, an instrumental variable (IV) estimator with instruments deviated from past means has the same asymptotic distribution as the infeasible optimal IV estimator when bothNandT, the dimensions of the cross section and time series, are large. If we assume that the errors are normally distributed, the asymptotic variance of the proposed IV estimator is shown to attain the lower bound when bothNandTare large. A simulation study is conducted to assess the estimator.

scholarly journals Quantile Regression with Clustered Data

2016 ◽  
Vol 5 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Paulo M.D.C. Parente ◽  
João M.C. Santos Silva
Keyword(s):  
Quantile Regression ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Consistent Estimator ◽  
Regression Estimator ◽  
Finite Sample ◽  
Specification Test ◽  
Asymptotically Normal ◽  
Cluster Correlation

AbstractWe study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.

The Asymptotic Distribution of the S–Gini Index

2002 ◽  
Vol 44 (4) ◽  
pp. 439-446 ◽  
Author(s):  
Ričardas Zitikis ◽  
Joseph L. Gastwirth
Keyword(s):  
Asymptotic Distribution ◽  
Gini Index

scholarly journals ESTIMATION FOR A NONSTATIONARY SEMI-STRONG GARCH(1,1) MODEL WITH HEAVY-TAILED ERRORS

2009 ◽  
Vol 26 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Oliver Linton ◽  
Jiazhu Pan ◽  
Hui Wang
Keyword(s):  
Asymptotic Distribution ◽  
Stationary Solution ◽  
Bootstrap Method ◽  
Sufficient Conditions ◽  
Domain Of Attraction ◽  
Local Minimizer ◽  
Stable Law ◽  
Moment Conditions ◽  
Least Absolute Deviations ◽  
Heavy Tailed

This paper studies the estimation of a semi-strong GARCH(1,1) model when it does not have a stationary solution, where semi-strong means that we do not require the errors to be independent over time. We establish necessary and sufficient conditions for a semi-strong GARCH(1,1) process to have a unique stationary solution. For the nonstationary semi-strong GARCH(1,1) model, we prove that a local minimizer of the least absolute deviations (LAD) criterion converges at the rate $\root \of n $ to a normal distribution under very mild moment conditions for the errors. Furthermore, when the distributions of the errors are in the domain of attraction of a stable law with the exponent κ ∈ (1, 2), it is shown that the asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is non-Gaussian but is some stable law with the exponent κ ∈ (0, 2). The asymptotic distribution is difficult to estimate using standard parametric methods. Therefore, we propose a percentile-t subsampling bootstrap method to do inference when the errors are independent and identically distributed, as in Hall and Yao (2003). Our result implies that the least absolute deviations estimator (LADE) is always asymptotically normal regardless of whether there exists a stationary solution or not, even when the errors are heavy-tailed. So the LADE is more appealing when the errors are heavy-tailed. Numerical results lend further support to our theoretical results.

Minor Concentration Ratios for the Bounds of the Gini Index

2004 ◽  
Author(s):  
Tomson Ogwang
Keyword(s):  
Gini Index ◽  
Concentration Ratio ◽  
The United States ◽  
Grouped Data ◽  
Lower And Upper Bounds ◽  
Income Distributions ◽  
The Lorenz Curve ◽  
Distribution Studies ◽  
Minor Concentration ◽  
Concentration Ratios

The minor concentration ratio is used to supplement the Gini index in income distribution studies. The appeal of the minor concentration ratio stems form the fact that it examines the relative position of the “poor”, an important focus group in the analysis of income distributions. In this note, minor concentration ratios associated with the lower and upper bounds of the Gini index are derived based on the observed points of the Lorenz curve. When the two minor concentration ratios are computed using grouped data for the United States, they turn out to be fairly close.

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