Horseshoe shrinkage methods for Bayesian fusion estimation

Adaptive Bayesian Shrinkage Estimation Using Log-Scale Shrinkage Priors

Global-local shrinkage hierarchies are an important, recent innovation in Bayesian estimation of regression models. In this paper we propose to use log-scale distributions as a basis for generating familes of flexible prior distributions for the local shrinkage hyperparameters within such hierarchies. An important property of the log-scale priors is that by varying the scale parameter one may v...

Shrinkage methods for instrumental variable estimation∗

This paper proposes shrinkage methods for instrumental variable estimation to solve the “many instruments” problem. Even though using a large number of instruments reduces the asymptotic variances of the estimators, it has been observed both in theoretical works and in practice that in finite samples the estimators may behave very poorly if the number of instruments is large. This problem can b...

Bayesian Masking: Sparse Bayesian Estimation with Weaker Shrinkage Bias

A common strategy for sparse linear regression is to introduce regularization, which eliminates irrelevant features by letting the corresponding weights be zeros. However, regularization often shrinks the estimator for relevant features, which leads to incorrect feature selection. Motivated by the above-mentioned issue, we propose Bayesian masking (BM), a sparse estimation method which imposes ...

Double shrinkage empirical Bayesian estimation for unknown and unequal variances

In this paper, we construct a point estimator when assuming unequal and unknown variances by using the empirical Bayes approach in the classical normal mean problem. The proposed estimator shrinks both means and variances, and is thus called the double shrinkage estimator. Extensive numerical studies indicate that the double shrinkage estimator has lower Bayes risk than the estimator which shri...

Bayesian Methods for Function Estimation