Single Imputation Methods and Confidence Intervals for the Gini Index

Mathematics

Juan F. Muñoz-Rosas¹  Pablo J. Moya-Fernández¹  Encarnación Álvarez-Verdejo¹ 

[1] Department of Quantitative Methods in Economics and Business, University of Granada, 18011 Granada, Spain;

关键词: missing data;    variance estimation;    coverage;    inequality;    non-response mechanism;   

DOI  :  10.3390/math9243252

来源: DOAJ

【 摘 要 】

The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods when they are applied to the estimation of the Gini index, a popular measure of inequality used in many studies. Various methods for constructing confidence intervals for the Gini index are also empirically evaluated. We consider several empirical measures to analyse the performance of estimators and confidence intervals, allowing us to quantify the magnitude of the non-response bias problem. We find extremely large biases under certain non-response mechanisms, and this problem gets noticeably worse as the proportion of missing data increases. For a large correlation coefficient between the target and auxiliary variables, the regression imputation method may notably mitigate this bias problem, yielding appropriate mean square errors. We also find that confidence intervals have poor coverage rates when the probability of data being missing is not uniform, and that the regression imputation method substantially improves the handling of this problem as the correlation coefficient increases.

【 授权许可】

Unknown