A theoretical note on optimal sufficient dimension reduction with singularity

Jae Keun Yoo

doi:10.1016/j.spl.2015.01.004

A theoretical note on optimal sufficient dimension reduction with singularity

Jae Keun Yoo

Department of Statistics

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

1 Scopus citations

Abstract

In this paper, we discuss an optimal sufficient dimension reduction through minimizing a quadratic objective function proposed by Cook and Ni (2005) with singular inner-product matrix. Within a less restrictive class of inner-product matrices, a generalized inverse of the consistent estimator of the asymptotic covariance matrix gives us the benefit of χ² statistic and asymptotic efficiency within a subclass.

Original language	English
Pages (from-to)	109-113
Number of pages	5
Journal	Statistics and Probability Letters
Volume	99
DOIs	https://doi.org/10.1016/j.spl.2015.01.004
State	Published - 1 Apr 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Keywords

Minimum discrepancy approach
Singularity
Sufficient dimension reduction
χ test

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10.1016/j.spl.2015.01.004

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AB - In this paper, we discuss an optimal sufficient dimension reduction through minimizing a quadratic objective function proposed by Cook and Ni (2005) with singular inner-product matrix. Within a less restrictive class of inner-product matrices, a generalized inverse of the consistent estimator of the asymptotic covariance matrix gives us the benefit of χ2 statistic and asymptotic efficiency within a subclass.

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KW - Singularity

KW - Sufficient dimension reduction

KW - χ test

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DO - 10.1016/j.spl.2015.01.004

M3 - Article

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VL - 99

SP - 109

EP - 113

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

A theoretical note on optimal sufficient dimension reduction with singularity

Abstract

Bibliographical note

Keywords

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