A Comprehensive Bayesian Framework for Envelope Models

• 成果类型: Article
• 署名作者: Chakraborty, Saptarshi; Su, Zhihua
• 署名单位: State University of New York (SUNY) System; University at Buffalo, SUNY; State University System of Florida; University of Florida
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2250096
• 发表日期: 2024
• 页码: 2129-2139
• 关键词: efficient estimation; variable selection; markov-chains; regression; binary

摘要

The envelope model aims to increase efficiency in multivariate analysis by using dimension reduction techniques. It has been used in many contexts including linear regression, generalized linear models, matrix/tensor variate regression, reduced rank regression, and quantile regression, and has shown the potential to provide substantial efficiency gains. Virtually all of these advances, however, have been made from a frequentist perspective, and the literature addressing envelope models from a Bayesian point of view is sparse. The objective of this article is to propose a Bayesian framework that is applicable across various envelope model contexts. The proposed framework aids straightforward interpretation of model parameters and allows easy incorporation of prior information. We provide a simple block Metropolis-within-Gibbs MCMC sampler for practical implementations of our method. Simulations and data examples are included for illustration. Supplementary materials for this article are available online.