分布变点模型的非参数检验和区间估计  

NONPARAMETRIC STATISTICAL INFERENCE FOR DISTRIBUTION CHANGE POINT MODEL

作　　者：谭智平[1] 缪柏其[1] 

机构地区：[1]中国科学技术大学统计与金融系,合肥230026

出　　处：《数学年刊（A辑）》2001年第5期617-626,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10071082);教育部博士点基金资助的项目.

摘　　要：提 要设　是定义在［０，１］上的随机过程Ｘ（ｔ）的ｎ个等距独立观察值，其中，　服从公共连续分布Ｆ；，服从公共连续分布 Ｆ＊，Ｆ与Ｆ＊不同；其中，是过程 Ｘ（ｔ）的变点．用ＣＵＳＵＭ及Ｂｒｏｗｎｉａｎ Ｓｈｅｅｔ方法给出了检测变点τ位置的一个程序，并证明了所得结果是强相合的；同时也讨论了τ的假设检验和区间估计．Let X be independent observations that come from a stochastic process and are taken on equal-paced t values, where have common continuous distribution F, and have another common continuous distribution F*. τ refers to the change point of this process. Some nonparametric procedures to detect the change point τ are proposed by means of CUSUM and Brownian sheet. Asymptotically strongly consistent estimators of τ are given and the hypothesis test and interval estimation are also discussed.

关 键 词：变点 假设检验 BROWNIAN sheet方法 经验分布 区间估计 非参数检验 随机过程 

分 类 号：O212.7[理学—概率论与数理统计]