The empirical Bayes estimators of treatment effects in a factorial experiment were derived and their asymptotic properties were explored. It was shown that they were asymptotically optimal and the estimator of the scale parameter had a limiting gamma distribution while the estimators of the factor effects had a limiting multivariate normal distribution. A Bootstrap analysis was performed to ill...

In this paper, the statistical inference of the unknown parameters of a twoparameter inverse Weibull (IW) distribution based on the progressive Type-II censored sample has been considered. The maximum likelihood estimators cannot be obtained in explicit forms, hence the approximate maximum likelihood estimators are proposed, which are in explicit forms. The Bayes and generalized Bayes estimator...

Based on the notion of predictive influence functions, the paper develops multivariate limited translation hierarchical Bayes estimators of the normal mean vector which serve as a compromise between the hierarchical Bayes and maximum likelihood estimators. The paper demonstrates the superiority of the limited translation estimators over the usual hierarchical Bayes estimators in terms of the fr...

X1, . . . , Xn iid ∼ N (θ, σ), with σ known. Our goal is to estimate θ under squared-error loss. For our first guess, pick the natural estimator X. Note that it has constant risk σ 2 n , which suggests minimaxity because we know that Bayes estimators with constant risk are also minimax estimators. However, X is not Bayes for any prior, because under squared-error loss unbiased estimators are Ba...

This paper considers inference under progressive type II censoring with a compound Rayleigh failure time distribution. The maximum likelihood (ML), and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters, namely reliability and hazard functions. We obtained Bayes estimators using the conjugate priors for two shape and scale parameters. When the two p...

This paper deals with the problem of selecting good negative binomial populations as compared with a standard or a control. The main results are based on the use of the empirical Bayes approach. First we derive the monotone empirical Bayes estimators of the concerned parameters. Based on these estimators, we construct monotone empirical Bayes selection rules. Asymptotic optimality properties of...

• In this paper, we propose Bayes estimators of the parameter of the exponentiated gamma distribution and associated reliability function under General Entropy loss function for a censored sample. The proposed estimators have been compared with the corresponding Bayes estimators obtained under squared error loss function and maximum likelihood estimators through their simulated risks (average l...