Admissibility of some preliminary test estimators for the mean of normal distribution (Q802228)

Let a random variable X follow a p-variate normal distribution \(N_ p(\theta,I_ p)\) with an unknown \(p\times 1\) vector \(\theta\) and \(p\times p\) identity matrix \(I_ p\). The admissibility of a preliminary test estimator using AIC (Akaike's information criterion) procedure will be shown if \(p=1\) and its inadmissibility will be shown if \(p\geq 3\) under the loss function based on Kullback-Leibler information measure. Furthermore the two sample case is also considered.