Dimension Reduction in Regressions Through Cumulative Slicing Estimation

• 成果类型: Article
• 署名作者: Zhu, Li-Ping; Zhu, Li-Xing; Feng, Zheng-Hui
• 署名单位: Shanghai University of Finance & Economics; Hong Kong Baptist University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09666
• 发表日期: 2010
• 页码: 1455-1466
• 关键词: sliced inverse regression; diverging number; asymptotics

摘要

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p = O(n(1/2)/log n) and the asymptotic normality for p = o(n(1/2)) are established, where p is the dimension of the predictors and n is sample size. Such asymptotic results improve the rate p = o(n(1/3)) in many existing contexts of semiparametric modeling. In addition, we propose a modified BIC-type criterion to estimate the structural dimension of the central subspace. Its consistency is established when p = o(n(1/2)). Extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration.