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

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.