JSM 2005 - Toronto

Abstract #303884

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 484
Type: Contributed
Date/Time: Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #303884
Title: Asymptotics for Sliced Average Variance Estimation
Author(s): Yingxing Li*+ and Lixing Zhu
Companies: The University of Hong Kong and The University of Hong Kong
Address: Dept. of Statistics, Hong Kong, 00000, Hong Kong
Keywords: Dimension reduction ; Sliced average variance estimation ; Asymptotic ; Convergence rate
Abstract:

In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal the asymptotic behavior is different from sliced inverse regression (SIR). The SIR can achieve the root n consistency even when each slice only contains two data points. However, when the response is continuous, the SAVE cannot be root n consistent or consistent when each slice contains a fixed number of data points not depending on n, where n is the sample size. These results confirm the folklore that the SAVE is more sensitive to the number of slices than is the SIR. Taking this into account, a bias correction is recommended to allow the root n consistency. In contrast, when the response is discrete taking finite values, the root n consistency can be achieved. Therefore, an approximation through discretization is studied, which is commonly used in practice. A simulation study is carried out for illustration.

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