Asymptotics for kernel estimation of slicing average third-moment estimation

Li Ping Zhu; Lixing ZHU

doi:10.1007/s10255-005-0290-3

Asymptotics for kernel estimation of slicing average third-moment estimation

Li Ping Zhu^*
, Lixing ZHU

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression^[7] (SIR), Sliced Average Variance Estimation^[4] (SAVE) and Slicing Average Third-moment Estimation^[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.

Original language	English
Pages (from-to)	103-114
Number of pages	12
Journal	Acta Mathematicae Applicatae Sinica
Volume	22
Issue number	1
DOIs	https://doi.org/10.1007/s10255-005-0290-3
Publication status	Published - Jan 2006

User-Defined Keywords

Asymptotic normality
Bandwidth selection
Dimension reduction
Inverse regression method
Kernel estimation

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10.1007/s10255-005-0290-3

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title = "Asymptotics for kernel estimation of slicing average third-moment estimation",

abstract = "To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.",

keywords = "Asymptotic normality, Bandwidth selection, Dimension reduction, Inverse regression method, Kernel estimation",

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

note = "Funding Information: Manuscript received April 22, 2005. Revised August 8, 2005. Supported by PhD Program Scholarship Fund of ECNU 2005, PhD Candidate Fund of ECNU for overseas Studies, International Conferences and Domestic Scholarly Visits, Shanghai, a grant (HKU 7058/05P) from the Research Grants Council of Hong Kong, Hong Kong, and a FRG grant (FRG/05-06/II-02) from Hong Kong Baptist University, Hong Kong, China.",

year = "2006",

month = jan,

doi = "10.1007/s10255-005-0290-3",

language = "English",

volume = "22",

pages = "103--114",

journal = "Acta Mathematicae Applicatae Sinica",

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T1 - Asymptotics for kernel estimation of slicing average third-moment estimation

AU - Zhu, Li Ping

AU - ZHU, Lixing

N1 - Funding Information: Manuscript received April 22, 2005. Revised August 8, 2005. Supported by PhD Program Scholarship Fund of ECNU 2005, PhD Candidate Fund of ECNU for overseas Studies, International Conferences and Domestic Scholarly Visits, Shanghai, a grant (HKU 7058/05P) from the Research Grants Council of Hong Kong, Hong Kong, and a FRG grant (FRG/05-06/II-02) from Hong Kong Baptist University, Hong Kong, China.

PY - 2006/1

Y1 - 2006/1

N2 - To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.

AB - To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.

KW - Asymptotic normality

KW - Bandwidth selection

KW - Dimension reduction

KW - Inverse regression method

KW - Kernel estimation

UR - https://www.scopus.com/pages/publications/29144474274

U2 - 10.1007/s10255-005-0290-3

DO - 10.1007/s10255-005-0290-3

M3 - Journal article

AN - SCOPUS:29144474274

SN - 0168-9673

VL - 22

SP - 103

EP - 114

JO - Acta Mathematicae Applicatae Sinica

JF - Acta Mathematicae Applicatae Sinica

IS - 1

ER -

Asymptotics for kernel estimation of slicing average third-moment estimation

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