Random Weighting Empirical Distribution Function and its Applications to Goodness-of-Fit Testing

Abstract

In this article, a randomized estimator of the empirical distribution function (EDF) called random weighting empirical distribution function (RWEDF) is introduced, one special case of which is just equivalent to the Bayesian bootstrap. The consistency of the RWEDF is established under certain conditions. By substituting this new EDF for the classical EDF, we obtain new versions of some EDF test statistics for goodness-of-fit. The simulation results show that the new tests are more powerful than the corresponding tests based on the classical EDF under some cases.

Keywords:

• EDF
• Goodness-of-fit test
• Power performance
• Random weighting

Mathematics Subject Classification:

• 62G10

Acknowledgment

The authors are grateful to the reviewers and the Editor-in-Chief for their valuable comments and suggestions.

Funding

Daojiang He's work is supported by the National Natural Science Foundation of China (Grant Nos. 11201005, 11271020), the Key Project of National Bureau of Statistics (Grant No. 2013LZ17), and the Natural Science Foundation of Anhui Province (No. 1308085QA13); Xingzhong Xu's work is supported by the National Natural Science Foundation of China (Grant No. 11071015).