A nonparametric mixture model approach to empirical Bayes compound decisions for the Gaussian location model is compared with a parametric empirical Bayes approach recently suggested by Martin and Walker and several recent more formal Bayes procedures. Martin and Walker (2013) have recently proposed a parametric empirical Bayes procedure for the classical Gaussian compound decision problem in w...

This paper provides the estimation of the scale parameter of the exponential distribution under multiply type-II censoring. Using generalized non-informative prior and natural conjugate prior, Bayes estimator and approximate Bayes estimators of the scale parameter have been obtained under square error loss function. The proposed Bayes estimators and approximate Bayes estimators are compared wit...

In this research, an iterative approach is employed to recognize and classify control chart patterns. To do this, by taking new observations on the quality characteristic under consideration, the Maximum Likelihood Estimator of pattern parameters is first obtained and then the probability of each pattern is determined. Then using Bayes’ rule, probabilities are updated recursively. Finally, when...

In “Efficient Estimation of Time Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects,” Plümper and Troeger (2007), propose a three step procedure for the estimation of fixed effects models that, it is claimed, “provides the most reliable estimates under a wide variety of specifications common to real world data.” Their FEVD estimator is startlingly si...

This paper devoted a Bayesian and non-Bayesian estimation of the stress-strength reliability, , when X and Y two independent Type I generalized logistic distribution with common scale parameter. The maximum likelihood estimator and Bayes estimator are proposed for the stress strength reliability based on lower record values. The Bayesian and non-Bayesian confidence intervals for the reliability...

In this paper, we examine the problem of estimating the sensitive characteristics and behaviors in a multinomial randomized response model using Bayesian approach. We derived a posterior distribution for parameter of interest for multinomial randomized response model. Based on the posterior distribution, we also calculated a credible intervals and mean squared error (MSE). We finally compare th...

In this paper we propose a generalised iterative algorithm for calculating variational Bayesian estimates for a normal mixture model and we investigate its convergence properties. It is shown theoretically that the variational Bayes estimator converges locally to the maximum likelihood estimator at the rate of O(1/n) in the large sample limit. We also demonstrate by numerical experiments that t...

In the first part of the course, we focused on optimal inference in the setting of point estimation (see Figure 12.2). We formulated this problem in the framework of decision theory and focused on finite sample criteria of optimality. We immediately discovered that uniform optimality was seldom attainable in practice, and thus, we developed our theory of optimality along two lines: constraining...