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...

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...

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function when 2 is known and unknown. We show that the usual estimator X is minimax and obtain a class of minimax estimators which have uniformly smaller risk than the usual estimator X. Also, we obtain the proper Bayes estimator relative to balanced loss function and nd the minim...

Consider the problem of estimating normal means from independent observations with known variances, possibly different from each other. Suppose that a second-level normal model is specified on the unknown means, with the prior means depending on a vector of covariates and the prior variances constant. For this two-level normal model, existing empirical Bayes methods are constructed from the Bay...

We investigate the asymptotic properties of the maximum likelihhod estimator and Bayes estimator of the drift parameter for stochastic processes satisfying a linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

This note considers estimation of the mean of a multivariate Gaussian distribution with known variance within the Minimum Message Length (MML) framework. Interestingly, the resulting MML estimator exactly coincides with the positive-part JamesStein estimator under the choice of an uninformative prior. A new approach for estimating parameters and hyperparameters in general hierarchical Bayes mod...

The hierarchical normal-normal model considered. Standard Empirical Bayes methods underestimate variability because they ignore uncertainty about the hyperparameters. Bayes' theorem solves this problem. We provide fast, exact inference that requires only a simple, univariate numerical integration to obtain the posterior distribution of the means. However, when standard, scale-invariant, vague p...