KULLBACK-LEIBLER AGGREGATION AND MISSPECIFIED GENERALIZED LINEAR MODELS

• 成果类型: Article
• 署名作者: Rigollet, Philippe
• 署名单位: Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS961
• 发表日期: 2012
• 页码: 639-665
• 关键词: statistical view; Optimal Rates; regression; persistence; selection

摘要

In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the parameter or even that the model on the systematic component is true. It is shown that this problem can be solved by constrained and/or penalized likelihood maximization and we derive sharp oracle inequalities that hold both in expectation and with high probability. Finally all the bounds are proved to be optimal in a minimax sense.