Shrinkage estimation with a matrix loss function

Consider estimating an n×p matrix of means Θ, say, from an n×p matrix of observations X, where the elements of X are assumed to be independently normally distributed with E(xij)=θij and constant variance, and where the performance of an estimator is judged using a p×p matrix quadratic error loss function. A matrix version of the James-Stein estimator is proposed, depending on a tuning constant a. It is shown to dominate the usual maximum likelihood estimator for some choices of a when n≥3. This result also extends to other shrinkage estimators and settings

Minimax estimation of constrained parametric functions for discrete families of distributions

Minimax estimation, Restricted parameter space, Discrete distributions, Squared error loss, Zero count probability, Odds-ratio, Binomial variance, Negative Binomial variance,

Computation of reference Bayesian inference for variance components in longitudinal studies

Bayesian, GLMM, Jeffreys’ prior, PQL, Reference prior, Uniform shrinkage prior, Variance component,