Empirical likelihood test for equality of two distributions using distance of characteristic functions

ABSTRACT

In this paper, we investigate the problem of testing for the equality of two distributions. We employ a two-sample Jackknife Empirical Likelihood (JEL) approach to construct a test statistic whose limiting distribution is Chi-square distribution with degree of freedom 1, no matter what the data dimension (fixed) is. A variety of synthetic data experiments demonstrate that our JEL test statistic performs very well, with a very neat asymptotic distribution under the null hypothesis. Furthermore, we apply the test procedure to a real dataset to obtain competitive results.

Keywords:

• Jackknife
• empirical likelihood
• U-statistics
• characteristic function

Acknowledgements

We wish to thank the editor, associate editor, and two anonymous referees for their detailed and constructive comments that led to significant improvements of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Zhi LIU  http://orcid.org/0000-0003-3861-1336

Notes

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Additional information

Funding

Zhi Liu's work is partially supported by Science and Technology Development Fund of Macau (127/2016/A3, 202/2017/A3).