基于block bootstrap的厚尾相依序列均值变点检验  

Block bootstrap tests for the mean change point with heavy-tailed dependent sequence

作　　者：秦瑞兵[1] 杨晓琴 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《贵州师范大学学报（自然科学版）》2017年第5期56-59,共4页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金(11226217;71501115);中国博士后基金面上项目(2012M510772);中国博士后基金特别资助项目(2013T60266)

摘　　要：针对无穷方差重尾相依序列的均值变点检验问题,基于序列自正则方法构造CUSUM型统计量,并在原假设下得到其渐近分布,在备择假设下得到检验的容许性。由于其渐近分布依赖于尾指数κ,且考虑到序列之间具有相依性,提出基于残差的block bootstrap方法。蒙特卡洛模拟表明该检验统计量和该抽样方法的有效性。To deal with the detection of the change in the mean of the heavy-tailed dependent observations with infinite variances,a CUSUM type test is proposed on the basis of the selfnormalized observations.The asymptotic distribution is obtained under the null hypothesis and the consistence of the test is established under the alternative hypothesis.Since the asymptotic distribution depends on the tail indexκ,a residual-based block bootstrap method is proposed to approximate the asymptotic null distribution.Monte Carlo simulations demonstrate the performance of the proposed test and the validity of the bootstrap method.

关 键 词：重尾 BLOCK BOOTSTRAP CUSUM检验 变点 自正则化 

分 类 号：O212.1[理学—概率论与数理统计]