Some Goodness of Fit Tests based on Centre Outward Spacings

TL;DR

This paper introduces univariate goodness of fit tests based on centre-outward spacings derived from data depth, showing they perform better for light-tailed symmetric alternatives compared to traditional spacing-based tests.

Contribution

It proposes new goodness of fit tests using centre-outward spacings, extending data depth concepts and demonstrating improved performance in specific cases.

Findings

Tests have similar asymptotic properties to traditional spacing tests.

Proposed tests outperform traditional ones for light-tailed symmetric alternatives.

Simulation results support the effectiveness of the new tests.

Abstract

Data depth provides a centre-outward ordering for multivariate data. Recently, some univariate GoF tests based on data depth have been studied by Li (2018). This paper discusses some univariate goodness of fit tests based on centre-outward spacings. These tests have similar asymptotic properties (distribution and efficiency) as those based on usual spacings. A simulation study reveals that for light-tailed symmetric alternatives, the proposed tests perform better than those based on usual spacings.