Asymptotic properties of goodness of fit tests based on higher order overlapping spacings

TL;DR

This paper investigates the asymptotic behavior of goodness-of-fit tests for uniformity that utilize higher order overlapping spacings, revealing how their local power depends on the properties of disjoint spacings as sample size grows.

Contribution

It introduces an analysis of the asymptotic properties of tests based on overlapping spacings with diverging order, highlighting their dependence on disjoint spacings.

Findings

Asymptotic local power depends on disjoint spacings properties.

Higher order overlapping spacings can diverge with sample size.

The study provides theoretical insights into the behavior of these tests.

Abstract

The paper is devoted to tests for uniformity based on sum-functions of overlapping spacings, where the order of spacings can diverge to infinity as the sample size increases. In particular, it is shown that the asymptotic local power of these tests depends significantly on the asymptotic properties of the counterpart statistics based on disjoint spacings.