An extended class of minimax generalized Bayes estimators of regression coefficients

TL;DR

This paper develops a broad class of minimax generalized Bayes estimators for regression coefficients in linear models with spherically symmetric errors, extending previous work to include non-monotone shrinkage functions, under invariant quadratic loss.

Contribution

It introduces a new, more general class of estimators that improve upon prior models by allowing non-monotone shrinkage functions in the minimax generalized Bayes framework.

Findings

The new estimators are minimax under invariant quadratic loss.

They include non-monotone shrinkage functions, broadening applicability.

The estimators outperform existing methods in certain scenarios.

Abstract

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman (2005) to include non-monotone shrinkage functions.