A robust inverse regression estimator

Liqiang Ni; R. Dennis Cook

doi:10.1016/j.spl.2006.07.018

A robust inverse regression estimator

Liqiang Ni, R. Dennis Cook

Statistics (Twin Cities)

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

6 Scopus citations

Abstract

A family of dimension reduction methods was developed by Cook and Ni [Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Amer. Statist. Assoc. 100, 410-428.] via minimizing a quadratic objective function. Its optimal member called the inverse regression estimator (IRE) was proposed. However, its calculation involves higher order moments of the predictors. In this article, we propose a robust version of the IRE that only uses second moments of the predictor for estimation and inference, leading to better small sample results.

Original language	English (US)
Pages (from-to)	343-349
Number of pages	7
Journal	Statistics and Probability Letters
Volume	77
Issue number	3
DOIs	https://doi.org/10.1016/j.spl.2006.07.018
State	Published - Feb 1 2007

Bibliographical note

Funding Information:
This research was supported in part by National Science Foundation Grant DMS-0405360.

Keywords

Central subspace
Inverse regression estimator
Sufficient dimension reduction

Publisher link

10.1016/j.spl.2006.07.018

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abstract = "A family of dimension reduction methods was developed by Cook and Ni [Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Amer. Statist. Assoc. 100, 410-428.] via minimizing a quadratic objective function. Its optimal member called the inverse regression estimator (IRE) was proposed. However, its calculation involves higher order moments of the predictors. In this article, we propose a robust version of the IRE that only uses second moments of the predictor for estimation and inference, leading to better small sample results.",

keywords = "Central subspace, Inverse regression estimator, Sufficient dimension reduction",

author = "Liqiang Ni and Cook, {R. Dennis}",

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AU - Cook, R. Dennis

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N2 - A family of dimension reduction methods was developed by Cook and Ni [Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Amer. Statist. Assoc. 100, 410-428.] via minimizing a quadratic objective function. Its optimal member called the inverse regression estimator (IRE) was proposed. However, its calculation involves higher order moments of the predictors. In this article, we propose a robust version of the IRE that only uses second moments of the predictor for estimation and inference, leading to better small sample results.

AB - A family of dimension reduction methods was developed by Cook and Ni [Sufficient dimension reduction via inverse regression: a minimum discrepancy approach. J. Amer. Statist. Assoc. 100, 410-428.] via minimizing a quadratic objective function. Its optimal member called the inverse regression estimator (IRE) was proposed. However, its calculation involves higher order moments of the predictors. In this article, we propose a robust version of the IRE that only uses second moments of the predictor for estimation and inference, leading to better small sample results.

KW - Central subspace

KW - Inverse regression estimator

KW - Sufficient dimension reduction

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JO - Statistics and Probability Letters

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IS - 3

ER -

A robust inverse regression estimator

Abstract

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Keywords

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