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正态分布方差变点的检验
引用本文:王静龙 Bhat.,MI.正态分布方差变点的检验[J].应用概率统计,1998,14(2):113-121.
作者姓名:王静龙 Bhat.  MI
作者单位:华东师范大学!上海(王静龙),Griffith大学!澳大利亚(M.IshaqBhatti)
摘    要:本文讨论了正态分布方差只有一个变点的检验问题,我们构造了三个检验统计量,其中L检验基于非参数U统计量,B检验基于Bayes方法,R检验由极大似然比方法导出.本文给出了L、B、R检验的渐近临界值,并用MonteCarlo模拟方法研究了这三个检验与平方的CUSUM检验以及LM检验的势,并进行了比较。当变点在序列的前一半位置时,L和R检验较好,当变点在序列的后一半位置时,平方的CUSUM和B检验较好.

关 键 词:正态随机序列  变点  U-统计量  Bayes方法  最大似然比

Three Tests for a Change-point in Variance of Normal Distribution
WANG JINGLONG, M. ISHAQ BHATTI.Three Tests for a Change-point in Variance of Normal Distribution[J].Chinese Journal of Applied Probability and Statisties,1998,14(2):113-121.
Authors:WANG JINGLONG  M ISHAQ BHATTI
Abstract:This paper considers the problem of testing for a change-point in variance of the sequence of normal random variables with unknown mean. We construct three tests, namely, L-test based on Lehmann's (1951) non-parametric U-statistic, B-test based on Bayesian method and R-test derived from the maximum likelihood ratio method. The approximate critical values of L, B, R tests are calculated. Monte Carlo simulation studies were carried out to calculate power of these tests, the CUSUM of squares test (Brown et al, 1975) and the LM-test (Nyblom, 1989). An empirical power comparison of the above tests suggests that when change-point is between the beginning and the mid portion, L and R tests are better, when changes-point is between the mid.portion and the end, CUSUM of squares and B tests are better.
Keywords:Normal random sequence  change-point  U-statistic  Bayesian methods  maximum likelihood ratio
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