scholarly journals The test and confidence interval for a change-point in mean vector of multivariate normal distribution

1994 ◽  
pp. 397-411
Author(s):  
Jing-Long Wang ◽  
Jin Wang
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Change Point ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Mean Vector

Estimators which are Uniformly Better than the James-Stein Estimator

1997 ◽  
Vol 47 (3-4) ◽  
pp. 167-180 ◽  
Author(s):  
Nabendu Pal ◽  
Jyh-Jiuan Lin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Multivariate Normal Distribution ◽  
Multivariate Normal ◽  
Likelihood Estimator ◽  
Mean Estimation ◽  
Stein Estimator ◽  
Mean Vector ◽  
Better Than

Assume i.i.d. observations are available from a p-dimensional multivariate normal distribution with an unknown mean vector μ and an unknown p .d. diaper- . sion matrix ∑. Here we address the problem of mean estimation in a decision theoretic setup. It is well known that the unbiased as well as the maximum likelihood estimator of μ is inadmissible when p ≤ 3 and is dominated by the famous James-Stein estimator (JSE). There are a few estimators which are better than the JSE reported in the literature, but in this paper we derive wide classes of estimators uniformly better than the JSE. We use some of these estimators for further risk study.

DISPERSIVE ORDERING FOR THE MULTIVARIATE NORMAL DISTRIBUTION

2016 ◽  
Vol 30 (2) ◽  
pp. 141-152
Author(s):  
Xuan Leng ◽  
Jinsen Zhuang ◽  
Taizhong Hu
Keyword(s):  
Normal Distribution ◽  
Random Vector ◽  
Order Statistic ◽  
Multivariate Normal Distribution ◽  
Random Variable ◽  
Multivariate Normal ◽  
Standard Normal ◽  
Dispersive Ordering ◽  
Mean Vector ◽  
Straightforward Proof

Let (X1, …, Xn) be a multivariate normal random vector with any mean vector, variances equal to 1 and covariances equal and positive. Turner and Whitehead [9] established that the largest order statistic max{X1, …, Xn} is less than the standard normal random variable in the dispersive order. In this paper, we give a new and straightforward proof for this result. Several possible extensions of this result are also discussed.

scholarly journals On sequential estimation of a certain estimable function of the mean vector of a multivariate normal distribution

1973 ◽  
Vol 15 (3) ◽  
pp. 291-295 ◽  
Author(s):  
V. K. Rohatgi ◽  
Suresh C. Rastogi
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Sequential Estimation ◽  
Stopping Rule ◽  
Diagonal Matrix ◽  
Multivariate Normal ◽  
The Mean ◽  
Mean Vector

Consider a k-variable normal distribution Ν (μ,Σ where mgr; = (μ1,μ2, … μk)' and Σ is diagonal matrix of unknown elements >0,i = 1,2, … k. The problem of sequential estimation of = 1 αiμi is considered. The stopping rule is shown to have some interesting limiting properties when the σi's become infinite.

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