ADAPTIVE NONPARAMETRIC BAYESIAN INFERENCE USING LOCATION-SCALE MIXTURE PRIORS

• 成果类型: Article
• 署名作者: de Jonge, R.; van Zanten, J. H.
• 署名单位: Eindhoven University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS811
• 发表日期: 2010
• 页码: 3300-3320
• 关键词: posterior convergence-rates; dirichlet mixtures; DENSITY-ESTIMATION; gaussian measures; Metric Entropy; distributions; approximation; Consistency; models

摘要

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly constructed. In particular, we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a Gaussian kernel, an inverse gamma bandwidth, and Gaussian mixing weights.