Mixing strategies for density estimation

• 成果类型: Article
• 署名作者: Yang, Y
• 署名单位: Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016120365
• 发表日期: 2000
• 页码: 75-87
• 关键词: model selection; Nonparametric Regression; INFORMATION; RISK; bounds

摘要

General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under Rullback-Leibler and squared L-2 losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks. A consequence is that under some mild conditions, an asymptotically minimax-rate adaptive estimator exists for a given countable collection of density classes; that is, a single estimator can be constructed to be simultaneously minimax-rate optimal for all the function classes being considered. A demonstration is given for high-dimensional density estimation on [0, 1](d) where the constructed estimator adapts to smoothness and interaction-order over some piecewise Besov classes and is consistent for all the densities with finite entropy.