Asymptotic Efficiency of Goodness-of-fit Tests Based on Too-Lin Characterization

TL;DR

This paper introduces a new class of uniformity tests based on Too-Lin characterization, analyzing their asymptotic properties, efficiencies, and power, with applications in time series analysis.

Contribution

It proposes a novel class of goodness-of-fit tests applicable to various null hypotheses, with detailed asymptotic analysis and efficiency comparisons.

Findings

Tests are applicable to simple and composite hypotheses.

Bahadur efficiencies are calculated for local alternatives.

Power study and applications in time series are provided.

Abstract

In this paper a new class of uniformity tests is proposed. It is shown that those tests are applicable to the cases of any simple null hypothesis as well as for the composite null hypothesis of rectangular distributions on arbitrary support. The asymptotic properties of test statistics are examined. The tests are compared with some standard and some recent uniformity tests. For each test the Bahadur efficiencies against some common local alternatives are calculated. A class of locally optimal alternatives is found for each proposed test. The power study is also provided. Some applications in time series analysis are presented.