NDLI: On spline approximation of sliced inverse regression

Content Provider	Springer Nature Link
Author	Zhu, Li ping Yu, Zhou
Copyright Year	2007
Abstract	The dimension reduction is helpful and often necessary in exploring the nonparametric regression structure. In this area, Sliced inverse regression (SIR) is a promising tool to estimate the central dimension reduction (CDR) space. To estimate the kernel matrix of the SIR, we herein suggest the spline approximation using the least squares regression. The heteroscedasticity can be incorporated well by introducing an appropriate weight function. The root-n asymptotic normality can be achieved for a wide range choice of knots. This is essentially analogous to the kernel estimation. Moreover, we also propose a modified Bayes information criterion (BIC) based on the eigenvalues of the SIR matrix. This modified BIC can be applied to any form of the SIR and other related methods. The methodology and some of the practical issues are illustrated through the horse mussel data. Empirical studies evidence the performance of our proposed spline approximation by comparison of the existing estimators.
Starting Page	1289
Ending Page	1302
Page Count	14
File Format	PDF
ISSN	10069283
Journal	Science in China Series A: Mathematics
Volume Number	50
Issue Number	9
e-ISSN	18622763
Language	English
Publisher	Science in China Press
Publisher Date	2007-06-26
Publisher Place	Beijing
Access Restriction	Subscribed
Subject Keyword	asymptotic normality spline Bayes information criterion dimension reduction sliced inverse regression structural dimensionality Estimation General nonlinear regression Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Partially linear estimation using sufficient dimension reduction

On sliced inverse regression with.

2009a Likelihood-based sufficient dimension reduction

Dimension reduction based on weighted variance estimate

Sliced inverse regression for dimension reduction (1991)

Sliced Regression for Dimension Reduction

Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation

Using Linear Smoothers to Assess Structural Dimension of Regressions (2003)

Sufficient dimension reduction via inverse regression a minimum discrepancy approach (2005)

On spline approximation of sliced inverse regression

Similar Documents

Partially linear estimation using sufficient dimension reduction

On sliced inverse regression with.

2009a Likelihood-based sufficient dimension reduction

Dimension reduction based on weighted variance estimate

Sliced inverse regression for dimension reduction (1991)

Sliced Regression for Dimension Reduction

Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation

Using Linear Smoothers to Assess Structural Dimension of Regressions (2003)

Sufficient dimension reduction via inverse regression a minimum discrepancy approach (2005)

On spline approximation of sliced inverse regression