Predictive Density Estimation for Multiple Regression

Penn collection
Statistics Papers
Degree type
Discipline
Subject
Bayesian prediction
model uncertainty
multiple shrinkage
prior distributions
shrinkage estimation
Statistics and Probability
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
George, Edward I
Xu, Xinyi
Contributor
Abstract

Suppose we observe X ~ Nm(Aβ, σ2I) and would like to estimate the predictive density p(y|β) of a future Y ~ Nn(Bβ, σ2I). Evaluating predictive estimates by Kullback–Leibler loss, we develop and evaluate Bayes procedures for this problem. We obtain general sufficient conditions for minimaxity and dominance of the “noninformative” uniform prior Bayes procedure. We extend these results to situations where only a subset of the predictors in A is thought to be potentially irrelevant. We then consider the more realistic situation where there is model uncertainty and this subset is unknown. For this situation we develop multiple shrinkage predictive estimators and obtain general minimaxity and dominance conditions. Finally, we provide an explicit example of a minimax multiple shrinkage predictive estimator based on scaled harmonic priors.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
2008-04-01
Journal title
Econometric Theory
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Recommended citation
Collection