Department of Statistics, Sultan Qaboos University, Muscat, Oman
Abstract: A Bayesian sequential procedure for estimating the parameter of a class of life distributions under the squared loss is proposed. It is assumed that the cost per observation is one unit and that the parameter is the value of a random variable having the Inverse Gamma distribution with known parameters. The procedure has two components, a stopping time and the Bayes estimator based on the observations taken up to the stopping time. An upper bound is obtained for the Bayes regret, that is used as a measure of the performance of the proposed. It is found that the proposed procedure performs better than the best fixed-sample-size procedure, asymptotically.
Keywords: Bayes estimator, Bayes regret, Jensen’s inequality, Fatou’s Lemma, martingale, posterior distribution, sequential procedure, stopping time
Pages: 15 – 25 | Full PDF Paper