Estimation of Gini Index within Pre-Specied Error Bound

TL;DR

This paper introduces a sequential method for estimating the Gini index with a guaranteed confidence level and margin of error, overcoming limitations of fixed sample size approaches.

Contribution

It develops a novel sequential procedure for constructing confidence intervals for the Gini index with specified accuracy and confidence, proving its optimality without distributional assumptions.

Findings

The proposed method achieves first order asymptotic efficiency.

It guarantees the confidence coefficient and margin of error in finite samples.

Theoretical properties are established without distributional assumptions.

Abstract

Gini index is a widely used measure of economic inequality. This article develops a general theory for constructing a confidence interval for Gini index with a specified confidence coefficient and a specified width. Fixed sample size methods cannot simultaneously achieve both the specified confidence coefficient and specified width. We develop a purely sequential procedure for interval estimation of Gini index with a specified confidence coefficient and a fixed margin of error. Optimality properties of the proposed method, namely first order asymptotic efficiency and asymptotic consistency are proved. All theoretical results are derived without assuming any specific distribution of the data.