厚尾序列均值变点的非参数检验

摘要

Aim To study a mean shift problem with k stable innovations in haavy-tail distribution. Methods A nonparametric test is proposed. Results Based on Wilcoxon rank-sum Statistic, the statistics for testing this change-point problem is constructed. Conclusion The asymptotic null distribution of the statistics is obtained. Besides, the consistency of this test under the alternative hypothesis is also proved.%目的 考虑稳定系数为κ的厚尾分布的均值变点检验问题.方法 利用非参数检验方法.结果 基于Wilcoxon秩和统计量,构造出了相应的检验统计量.结论 得到了原假设下统计量的渐近分布,并证明了在备择假设下统计量的相合性.