Asymptotics for pooled marginal slicing estimator based on SIR_α approach

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• 作者：Jé ; rô ; me Saracco
• 关键词：Asymptotics ; Dimension reduction subspaces ; Eigen-elements ; Pooled marginal slicing ; Semiparametric regression model ; Sliced inverse regression
• 刊名：Journal of Multivariate Analysis
• 出版年：2005
• 期刊代码：77_0047259x
• 类别：mt
• 出版时间：2005
• 卷：96
• 期：1
• 页码：117-135
• 文件大小：269 K

摘要

Pooled marginal slicing (PMS) is a semiparametric method, based on sliced inverse regression (SIR) approach, for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we consider the SIR_α version (combining the SIR-I and SIR-II approaches) of the PMS estimator and we establish the asymptotic distribution of the estimated matrix of interest. Then the asymptotic normality of the eigenprojector on the estimated effective dimension reduction (e.d.r.) space is derived as well as the asymptotic distributions of each estimated e.d.r. direction and its corresponding eigenvalue.