重尾序列均值变点的经验似然比检验

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

本文通过经验似然思想建立假设检验的方法,研究了重尾序列均值变点的检测问题.首先,基于重尾模型,在原假设和备择假设下得到经验似然函数.其次,基于经验似然函数构造似然比检验统计量,并给出在原假设成立时该似然比统计量的渐近分布.最后,进行~Monte Carlo~数值模拟验证该方法的有效性,模拟结果表明本方法对重尾序列均值变点的检测具有良好效果.

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.