Document Type
Journal Article
Department/Unit
Department of Mathematics
Title
On splines approximation for sliced average variance estimation
Language
English
Abstract
To avoid the inconsistency and slow convergence rate of the slicing estimator of the sliced average variance estimation (SAVE), particularly in the continuous response cases, we suggest B-spline approximation that can make the estimator sqrt(n) consistent and keeps the spirit of easy implementation that the slicing estimation shares. Compared with kernel estimation that has been used in the literature, B-spline approximation is of higher accuracy and is easier to implement. To estimate the structural dimension of the central dimension reduction space, a modified Bayes information criterion is suggested, which makes the leading term and the penalty term comparable in magnitude. This modified criterion can help to enhance the efficacy of estimation. The methodologies and theoretical results are illustrated through an application to the horse mussel data and simulation comparisons with existing methods by simulations. © 2008 Elsevier B.V. All rights reserved.
Keywords
Asymptotic normality, B-spline, Bayes information criterion, Dimension reduction, Sliced average variance estimation, Structural dimension
Publication Date
2009
Source Publication Title
Journal of Statistical Planning and Inference
Volume
139
Issue
4
Start Page
1493
End Page
1505
Publisher
Elservier
DOI
10.1016/j.jspi.2008.07.017
Link to Publisher's Edition
ISSN (print)
03783758
Recommended Citation
Yu, Zhou, Li-Ping Zhu, and Li-Xing Zhu. "On splines approximation for sliced average variance estimation." Journal of Statistical Planning and Inference 139.4 (2009): 1493-1505.