On sliced inverse regression with high-dimensional covariates

Lixing ZHU; Baiqi Miao; Heng PENG

doi:10.1198/016214505000001285

On sliced inverse regression with high-dimensional covariates

Lixing ZHU^*, Baiqi Miao, Heng PENG

^*Corresponding author for this work

Department of Mathematics

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

193 Citations (Scopus)

Abstract

Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.

Original language	English
Pages (from-to)	630-643
Number of pages	14
Journal	Journal of the American Statistical Association
Volume	101
Issue number	474
DOIs	https://doi.org/10.1198/016214505000001285
Publication status	Published - Jun 2006

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Central dimension-reduction subspaee
Convergence rate
Dimensionality determination
Sliced inverse regression

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10.1198/016214505000001285

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title = "On sliced inverse regression with high-dimensional covariates",

abstract = "Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.",

keywords = "Central dimension-reduction subspaee, Convergence rate, Dimensionality determination, Sliced inverse regression",

author = "Lixing ZHU and Baiqi Miao and Heng PENG",

note = "Funding Information: Lixing Zhu is Professor of Statistics, Department of Mathematics, Hong Kong Baptist University, and Cheung Kong Chair Professor at Renmin University of China under the Cheung Kong Scholars Program of the Ministry of Education and Li Ka Shing Foundation, Hong Kong, People{\textquoteright}s Republic of China (E-mail: lzhu@hkbu.edu.hk). Baiqi Miao is Professor, University of Science and Technology of China. Heng Peng is Post-Doctoral Fellow, Princeton University, Princeton, NJ 08544. This research was supported by a grant from the University Grants Council of Hong Kong (HKU7181/02H). The authors are grateful to the editor, an associate editor, and the two referees for their constructive comments and suggestions, which led to the great improvement of earlier draft. They also thank the associate editor and one of the referees for their generous help in improving the presentation of the article.",

year = "2006",

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doi = "10.1198/016214505000001285",

language = "English",

volume = "101",

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journal = "Journal of the American Statistical Association",

issn = "0162-1459",

publisher = "Taylor and Francis Ltd.",

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T1 - On sliced inverse regression with high-dimensional covariates

AU - ZHU, Lixing

AU - Miao, Baiqi

AU - PENG, Heng

N1 - Funding Information: Lixing Zhu is Professor of Statistics, Department of Mathematics, Hong Kong Baptist University, and Cheung Kong Chair Professor at Renmin University of China under the Cheung Kong Scholars Program of the Ministry of Education and Li Ka Shing Foundation, Hong Kong, People’s Republic of China (E-mail: lzhu@hkbu.edu.hk). Baiqi Miao is Professor, University of Science and Technology of China. Heng Peng is Post-Doctoral Fellow, Princeton University, Princeton, NJ 08544. This research was supported by a grant from the University Grants Council of Hong Kong (HKU7181/02H). The authors are grateful to the editor, an associate editor, and the two referees for their constructive comments and suggestions, which led to the great improvement of earlier draft. They also thank the associate editor and one of the referees for their generous help in improving the presentation of the article.

PY - 2006/6

Y1 - 2006/6

N2 - Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.

AB - Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.

KW - Central dimension-reduction subspaee

KW - Convergence rate

KW - Dimensionality determination

KW - Sliced inverse regression

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DO - 10.1198/016214505000001285

M3 - Journal article

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SN - 0162-1459

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EP - 643

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

IS - 474

ER -

On sliced inverse regression with high-dimensional covariates

Abstract

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