OPTIMAL MODEL SELECTION FOR DENSITY ESTIMATION OF STATIONARY DATA UNDER VARIOUS MIXING CONDITIONS

• 成果类型: Article
• 署名作者: Lerasle, Matthieu
• 署名单位: Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS888
• 发表日期: 2011
• 页码: 1852-1877
• 关键词: risk bounds; penalties

摘要

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are beta or tau-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.