Large deviations of U-empirical Kolmogorov-Smirnov tests, and their efficiency

TL;DR

This paper investigates the large deviation properties of U-empirical Kolmogorov-Smirnov tests under the null hypothesis, providing insights into their efficiency and applications in goodness-of-fit and symmetry testing.

Contribution

It characterizes the large deviation asymptotics of non-degenerate U-empirical KS tests and demonstrates how to compute their local Bahadur efficiency.

Findings

Large deviation asymptotics under the null hypothesis are described.

Methods for calculating local Bahadur efficiency are provided.

Applications to goodness-of-fit and symmetry tests are discussed.

Abstract

Non-degenerate U-empirical Kolmogorov-Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered. It is shown how to calculate their local Bahadur efficiency.