Article

Title: Minimum Risk Point Estimation of Gini Index

Author(s): Shyamal K.De and Bhargab Chattopadhyay
Issue: Volume 79 Series B Part 2 Year 2017
Pages: 247 -- 277
Abstract
This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost at the same time. In this article, a purely sequential procedure is proposed which provides an estimate of the sample size required to achieve a sufficiently smaller estimation error and lower sampling cost. Characteristics of the purely sequential procedure are examined and asymptotic optimality properties are proved without assuming any specific distribution of the data. Performance of our method is examined through extensive simulation study.
AMS (2000) subject classification. Primary: 62L12, 62G05; Secondary: 60G46, 60G40, 91B82.
Keywords and phrases: Asymptotic efficiency, Ratio regret, Reverse submartingale, Sequential point estimation, Simple random sampling, U-statistics