Structure adaptive approach for dimension reduction

• 成果类型: Article
• 署名作者: Hristache, M; Juditsky, A; Polzehl, J; Spokoiny, V
• 署名单位: Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1537-1566
• 关键词: principal hessian directions; regression

摘要

We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension in of the index space does not exceed 3, this space can be estimated with the rate n (-1/2) under rather mild assumptions on the model.