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.

Keywords:

• U-statistics
• bahadur efficiency
• conditional duration models
• moments of order statistics
• testing uniformity

2010 Mathematics Subject Classification::

• 60F10
• 62G10
• 62G20
• 62G30

Acknowledgments

We would like to thank the Referees for their useful remarks.

Additional information

Funding

This work was supported by the Ministry of Education, Science and Technological Development of Republic of Serbia under Grant 174012.