正态分布均值变点估计的收敛性

The convergence of the estimator for the change point in the mean of normal distribution

KoKoszka和Leipus先前讨论了独立序列中均值变点估计的相合性,而该文讨论了较为特殊的情形,即正态分布均值变点问题,利用CUSUM方法,研究了独立正态随机变量序列中方差不发生变化时,均值变点估计的相和性,并得到收敛速度.

The consistency of the estimators for the change point in the mean of dependent observations was obtained by Kokoszka and Leipus. In this paper, we studied a special case, and the change point problem in the mean of normal distribution was discussed, we studied the consistency of the estimator for the change point in the mean of independent normal random serials by use of CUSUM, when the variance didn＇t change. And we obtained the convergence rate for the estimator.