On the estimation of varextropy under complete data

TL;DR

This paper introduces nonparametric estimators for varextropy of continuous variables, proves their consistency, and demonstrates their effectiveness in uniformity testing through simulations.

Contribution

It presents new nonparametric estimators for varextropy, establishes their consistency, and develops uniformity tests with improved performance.

Findings

Estimators are consistent under regularity conditions.

Simulation results show estimators have low MSE and bias.

Varextropy-based tests outperform existing uniformity tests.

Abstract

In this paper, we propose nonparametric estimators for varextropy function of an absolutely continuous random variable. Consistency of the estimators is established under suitable regularity conditions. Moreover, a simulation study is performed to compare the performance of the proposed estimators based on mean squared error (MSE) and bias. Furthermore, by using the proposed estimators some tests are constructed for uniformity. It is shown that the varextropybased test proposed here performs well compared to the power of the other uniformity hypothesis tests.