On kernel method for sliced average variance estimation

Authors:
Li-Ping Zhu;Li-Xing Zhu
Affiliations:
East China Normal University, Shanghai, China and Hong Kong Baptist University, Hong Kong, China;East China Normal University, Shanghai, China and Hong Kong Baptist University, Hong Kong, China
Venue:
Journal of Multivariate Analysis
Year:
2007

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Abstract

In this paper, we use the kernel method to estimate sliced average variance estimation (SAVE) and prove that this estimator is both asymptotically normal and root n consistent. We use this kernel estimator to provide more insight about the differences between slicing estimation and other sophisticated local smoothing methods. Finally, we suggest a Bayes information criterion (BIC) to estimate the dimensionality of SAVE. Examples and real data are presented for illustrating our method.