Asymptotic efficiency of goodness-of-fit tests based on Too–Lin characterization

Abstract

In this article, 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.