Adaptive model selection

• 成果类型: Article
• 署名作者: Shen, XT; Ye, JM
• 署名单位: University System of Ohio; Ohio State University; City University of New York (CUNY) System; Baruch College (CUNY)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214502753479356
• 发表日期: 2002
• 页码: 210-221
• 关键词: choice

摘要

Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty per-forms well for small models and poorly for large models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed procedure, combining the benefit of a class of nonadaptive procedures, approximates the best performance of this class of procedures across a variety of different situations. This class includes many well-known procedures, such as AIC, BIC, Mallows's C-p, and risk inflation criterion (RIC). The proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression. Simulation results and an asymptotic analysis support the effectiveness of the proposed procedure.