We review historically the position of Sir R.A. Fisher towards Bayesian inference and, particularly, classical Bayes–Laplace paradigm. focus on his Fiducial Argument.

We study frequentist risk properties of predictive density estimators for mean mixtures multivariate normal distributions, involving an unknown location parameter θ∈Rd, and which include skew distributions. provide explicit representations Bayesian posterior densities, including the benchmark minimum equivariant (MRE) density, is minimax generalized Bayes with respect to improper uniform θ. For...

The goal of this thesis is to examine methods of statistical inference based on upper record values. This includes estimation of parameters based on samples of record values and prediction of future record values. We first define and discuss record times and record values and their distributions. Then we propose an efficient algorithm to generate random samples of record values. The algorithm, ...

This paper builds on a simple unified representation of shrinkage Bayes estimators based on hierarchical Normal-Gamma priors. Various popular penalized least squares estimators for shrinkage and selection in regression models can be recovered using this single hierarchical Bayes formulation. Using 129 U.S. macroeconomic quarterly variables for the period 1959 – 2010 I exhaustively evaluate the ...

In this paper, on the basis of a doubly censored sample and in a Bayesian framework, the problem of estimating the mean lifetime, hazard rate, and survival function of the exponential lifetime model is addressed. Bayes estimators under squared-error loss functions are obtained in closed forms. Highest posterior density (HPD) estimators and credible intervals are computed using iterative methods...

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...

Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...