Search results for "Normal location model"
showing 3 items of 3 documents
Sampling properties of the Bayesian posterior mean with an application to WALS estimation
2022
Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this pa…
Shrinkage efficiency bounds: An extension
2023
Hansen (2005) obtained the efficiency bound (the lowest achievable risk) in the p-dimensional normal location model when p≥3, generalizing an earlier result of Magnus (2002) for the one-dimensional case (p=1). The classes of estimators considered are, however, different in the two cases. We provide an alternative bound to Hansen's which is a more natural generalization of the one-dimensional case, and we compare the classes and the bounds.
Posterior moments and quantiles for the normal location model with Laplace prior
2021
We derive explicit expressions for arbitrary moments and quantiles of the posterior distribution of the location parameter η in the normal location model with Laplace prior, and use the results to approximate the posterior distribution of sums of independent copies of η.