On asymptotic efficiency of goodness-of-fit tests for the Pareto distribution based on its characterization

TL;DR

This paper introduces new goodness-of-fit tests for the Pareto distribution based on a novel characterization, analyzing their asymptotic properties, efficiency, and optimality.

Contribution

It presents a new characterization of the Pareto distribution and constructs novel tests with analyzed limiting behavior and efficiency.

Findings

Derived limiting distributions and large deviations for the new statistics

Calculated local Bahadur efficiency for parametric alternatives

Established conditions for local optimality of the tests

Abstract

We introduce a new characterization of Pareto distribution and construct integral and supremum type goodness-of-fit tests based on it. Limiting distribution and large deviations of new statistics are described and their local Bahadur efficiency for parametric alternatives is calculated. Conditions of local optimality of new statistics are given.