Some insights into continuum regression and its asymptotic properties

Xin Chen; R. Dennis Cook

doi:10.1093/biomet/asq024

Some insights into continuum regression and its asymptotic properties

Xin Chen, R. Dennis Cook

Statistics (Twin Cities)

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

4 Scopus citations

Abstract

Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter γ. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter γ. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary γ under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution.

Original language	English (US)
Pages (from-to)	985-989
Number of pages	5
Journal	Biometrika
Volume	97
Issue number	4
DOIs	https://doi.org/10.1093/biomet/asq024
State	Published - Dec 2010

Bibliographical note

Funding Information:
The authors would like to thank the editor, an associate editor and one anonymous referee for their constructive comments. This research was supported by the National Science Foundation, U.S.A.

Keywords

Central subspace
Continuum regression
Ordinary least squares
Partial least squares
Principal components
Sufficient dimension reduction

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10.1093/biomet/asq024

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abstract = "Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter γ. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter γ. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary γ under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution.",

keywords = "Central subspace, Continuum regression, Ordinary least squares, Partial least squares, Principal components, Sufficient dimension reduction",

author = "Xin Chen and Cook, {R. Dennis}",

note = "Funding Information: The authors would like to thank the editor, an associate editor and one anonymous referee for their constructive comments. This research was supported by the National Science Foundation, U.S.A.",

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T1 - Some insights into continuum regression and its asymptotic properties

AU - Chen, Xin

AU - Cook, R. Dennis

N1 - Funding Information: The authors would like to thank the editor, an associate editor and one anonymous referee for their constructive comments. This research was supported by the National Science Foundation, U.S.A.

PY - 2010/12

Y1 - 2010/12

N2 - Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter γ. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter γ. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary γ under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution.

AB - Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter γ. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter γ. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary γ under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution.

KW - Central subspace

KW - Continuum regression

KW - Ordinary least squares

KW - Partial least squares

KW - Principal components

KW - Sufficient dimension reduction

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SP - 985

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JO - Biometrika

JF - Biometrika

IS - 4

ER -

Some insights into continuum regression and its asymptotic properties

Abstract

Bibliographical note

Keywords

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