The empirical Bayes estimator of the probability of a successful event is deduced from mixed distributions. Specially, binomial and Poisson mixed distributions are analyzed. Some mixing distributions, well known in Reliability, Queuing Theory and other areas of Engineering, are considered. As it will be shown, a family of estimators with interesting characteristics is obtained for different mix...

The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed data will not be protected by the minimax property of shrinkage estimators such a" that of James and Stein, but instead will likely incur a greater error th...

Weibull distribution is widely employed in modeling and analyzing lifetime data. The present paper considers the estimation of the scale parameter of two parameter Weibull distribution with known shape. Maximum likelihood estimation is discussed. Bayes estimator is obtained using Jeffreys’ prior under linex loss function. Relative efficiency of the estimators are calculated in small and large s...

Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary informatio...

The problem of estimating the parameter θ, when it is restricted to an interval of the form [ ,1] m , in a class of discrete distributions, including Binomial ( , ), k θ Negative Binomial ( , ), r θ discrete Weibull ( ) θ and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of , θ with respect to a two points boundary supported prior is minimax unde...

In this article, we consider the problem of estimating the stress-strength reliability $Pr (X > Y)$ based on upper record values when $X$ and $Y$ are two independent but not identically distributed random variables from the power hazard rate distribution with common scale parameter $k$. When the parameter $k$ is known, the maximum likelihood estimator (MLE), the approximate Bayes estimator and ...

The problem of estimating a high-dimensional sparse vector θ ∈ R from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the well-known soft-thresholding estimator. We obtain concentration inequalities for the Stein’s unbiased ...

We investigate theoretically some properties of variational Bayes approximations based on estimating the mixing coefficients of known densities. We show that, with probability 1 as the sample size n grows large, the iterative algorithm for the variational Bayes approximation converges locally to the maximum likelihood estimator at the rate of O(1/n). Moreover, the variational posterior distribu...

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression model Y = Xβ+ ε, where Y is an m-vector of observations, X is a known m× k matrix, β is an unknown k-vector, and ε is anm-vector of unobservable random variables. The problem is squared error loss estimation of β based on some...