On kernel method for sliced average variance estimation

Li Ping Zhu; Lixing ZHU

doi:10.1016/j.jmva.2006.11.005

On kernel method for sliced average variance estimation

Li Ping Zhu, Lixing ZHU^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

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.

Original language	English
Pages (from-to)	970-991
Number of pages	22
Journal	Journal of Multivariate Analysis
Volume	98
Issue number	5
DOIs	https://doi.org/10.1016/j.jmva.2006.11.005
Publication status	Published - May 2007

Scopus Subject Areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

User-Defined Keywords

Asymptotic normality
Bandwidth selection
Dimension reduction
Kernel estimation
Sliced average variance estimation
Sliced inverse regression
Slicing estimation

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10.1016/j.jmva.2006.11.005

Cite this

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title = "On kernel method for sliced average variance estimation",

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.",

keywords = "Asymptotic normality, Bandwidth selection, Dimension reduction, Kernel estimation, Sliced average variance estimation, Sliced inverse regression, Slicing estimation",

author = "Zhu, {Li Ping} and Lixing ZHU",

note = "Funding Information: The research described here was supported by a Grant (HKBU 7058/05P) from the Research Grants Council of Hong Kong, and a Grant (FRG/05-06/II-02) from Hong Kong Baptist University, Hong Kong, China. ∗Corresponding author. Hong Kong Baptist University, Hong Kong, China. E-mail address: lzhu@hkbu.edu.hk (L.-X. Zhu).",

year = "2007",

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AU - ZHU, Lixing

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AB - 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.

KW - Asymptotic normality

KW - Bandwidth selection

KW - Dimension reduction

KW - Kernel estimation

KW - Sliced average variance estimation

KW - Sliced inverse regression

KW - Slicing estimation

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M3 - Article

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SN - 0047-259X

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SP - 970

EP - 991

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 5

ER -

On kernel method for sliced average variance estimation

Abstract

Scopus Subject Areas

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