Some improvement on non-parametric estimation of income distribution and poverty index

TL;DR

This paper introduces a bias-reduced kernel estimator for poverty measures that improves estimation accuracy of income distribution and poverty indices, with proven consistency and favorable simulation results.

Contribution

It presents a novel bias-reduced kernel estimator for the Foster-Greer-Thorbecke poverty measures, enhancing estimation accuracy over existing methods.

Findings

Estimator shows uniform almost sure consistency.

Estimator demonstrates uniform mean square consistency.

Simulation results indicate improved performance.

Abstract

In this paper, we propose an estimator of Foster, Greer and Thorbecke class of measures $\displaystyle P(z,\alpha) = \int_0^{z}\Big(\frac{z-x}{z}\Big)^{\alpha}f(x)\, dx$, where $z>0$ is the poverty line, $f$ is the probabily density function of the income distribution and $\alpha$ is the so-called poverty aversion. The estimator is constructed with a bias reduced kernel estimator. Uniform almost sure consistency and uniform mean square consistenty are established. A simulation study indicates that our new estimator performs well.