Empirical Likelihood Ratio Test for Mean Change-Point in Heavy-Tailed Sequence

This paper establishes a empirical likelihood method to detect change-point in the mean of heavy-tailed sequence. Firstly, under the null and the alternative hypothesis, the empirical likelihood functions are obtained in the heavy-tailed observations. Secondly, the empirical likelihood ratio statistics is constructed based on empirical likelihood functions. And under the null hypothesis, the asymptotic distribution of statistics is given. Finally, Monte Carlo simulation is carried out to verify the correctness of the method. The simulation results show that the performance of our method is well to detect mean change in heavy-tailed sequence.