Showing papers by "Palaniappan Vellaisamy published in 1988"
TL;DR: In this article, the natural selection rule for selecting the best populaton, that is, the one associated with the largest i, was considered, and the estimation of the mean of the selected population was considered.
Abstract: Let πi(i=1,2,…K) be independent U(0,⊝i) populations. Let Yi denote the largest observation based on a random sample of size n from the i-th population. for selecting the best populaton, that is the one associated with the largest ⊝i, we consider the natural selection rule, according to which the population corresponding to the largest Yi is selected. In this paper, the estimation of M. the mean of the selected population is considered. The natural estimator is positively biased. The UMVUE (uniformly minimum variance unbiased estimator) of M is derived using the (U,V)-method of Robbins (1987) and its asymptotic distribution is found. We obtain a minimax estimator of M for K≤4 and a class of admissible estimators among those of the form cYmax. For the case K = 2, the UMVUE is improved using the Brewster-Zidek (1974) Technique with respect to the squared error loss function L1 and the scale-invariant loss function L2. For the case K = 2, the MSE'S of all the estimators are compared for selected values of n a...
26 citations
TL;DR: In this paper, it is shown that the natural estimator is positively biased, and the uniformly minimum variance unbiased estimator (UMVE) of M is not minimax, while the minimazity of certain estimators of interest is investigated.
Abstract: Let л1 and л2 denote two independent gamma populations G(α1, p) and G(α2, p) respectively. Assume α(i=1,2)are unknown and the common shape parameter p is a known positive integer. Let Yi denote the sample mean based on a random sample of size n from the i-th population. For selecting the population with the larger mean, we consider, the natural rule according to which the population corresponding to the larger Yi is selected. We consider? in this paper, the estimation of M, the mean of the selected population. It is shown that the natural estimator is positively biased. We obtain the uniformly minimum variance unbiased estimator(UMVE) of M. We also consider certain subclasses of estikmators of the form c1x(1) +c1x(2) and derive admissible estimators in these classes. The minimazity of certain estimators of interest is investigated. Itis shown that p(p+1)-1x(1) is minimax and dominates the UMVUE. Also UMVUE is not minimax.
23 citations