Asymptotic Efficiency of Goodness-of-fit Tests for the Power Function Distribution Based on Puri--Rubin Characterization

TL;DR

This paper develops new goodness-of-fit tests for the power function distribution family using Puri-Rubin characterization, analyzing their asymptotic behavior and efficiency.

Contribution

It introduces integral and supremum type tests based on $U$-empirical processes and characterizes their asymptotic properties and local optimality.

Findings

Test statistics follow logarithmic large deviation asymptotics under null hypothesis.

Calculated local Bahadur efficiency under common alternatives.

Identified conditions for local optimality of the proposed tests.

Abstract

We construct integral and supremum type goodness-of-fit tests for the family of power distribution functions. Test statistics are functionals of $U-$empirical processes and are based on the classical characterization of power function distribution family belonging to Puri and Rubin. We describe the logarithmic large deviation asymptotics of test statistics under null-hypothesis, and calculate their local Bahadur efficiency under common parametric alternatives. Conditions of local optimality of new statistics are given.