Empirical likelihood ratio for two-sample compound Poisson processes under infinite second moment

Abstract

In this article, the author focus on the simple and yet very important case of making inference on the difference of two population means using the empirical likelihood approach of two sample compound Poisson process under infinite second moment. It is shown that the log empirical likelihood ratio statistic for the difference of two population means converges in distribution to ${\chi }_{(1)}^2$ as $n\to \infty .$ The simulation results show that the empirical likelihood ratio method is applicable under infinite second moment.

Keywords:

• Confidence interval
• empirical likelihood
• compound Poisson process
• two-sample
• domain of attraction of normal law

MR(2010) SUBJECT CLASSIFICATION:

• 62G20

Additional information

Funding

Cheng gratefully acknowledge financial support from Natural Science Foundation of Guangdong (2018A030313829), Characteristic Innovation Projects of Ordinary Universities of Guangdong (2019KTSCX202), the Higher Education Teaching Reform Project of Guangdong (2019625).