TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=29144474274&partnerID=8YFLogxK
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 -