A new estimator of Kullback–Leibler information based on a local linear regression and its application in goodness-of-fit tests

Abstract

We propose here a general statistic for the goodness-of-fit test of statistical models. The proposed statistic is constructed based on an estimate of Kullback–Leibler information. The properties of the proposed test are stated and then the established results are used to introduce goodness-of-fit tests for the normal and exponential distributions. A simulation study is carried out for examining the power of the proposed test and to compare it with those of some existing procedures. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can confidently apply in practice. Finally, some illustrative examples are presented and analysed, and concluding comments are made.

KEYWORDS:

• Information theory
• Kullback–Leibler information
• goodness-of-fit tests
• normal
• exponential
• Monte Carlo simulation
• test power

Acknowledgements

The authors are grateful to anonymous referees and the associate editor for providing some useful comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.