Minimum Risk Point Estimation of Gini Index

TL;DR

This paper introduces a sequential estimation method for the Gini index that optimally balances sampling cost and estimation accuracy, with proven asymptotic optimality and validated through simulations.

Contribution

It proposes a novel purely sequential procedure for Gini index estimation that minimizes both sampling cost and estimation error without distribution assumptions.

Findings

The method achieves asymptotic optimality.

It reduces sampling costs compared to fixed-sample methods.

Simulation results confirm effectiveness across distributions.

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.