Lassoing eigenvalues

David E. Tyler; Mengxi Yi

doi:10.1093/biomet/asz076

Lassoing eigenvalues

David E. Tyler, Mengxi Yi

School of Arts and Sciences, Statistics

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

2 Scopus citations

Abstract

The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

Original language	English (US)
Pages (from-to)	397-414
Number of pages	18
Journal	Biometrika
Volume	107
Issue number	2
DOIs	https://doi.org/10.1093/biomet/asz076
State	Published - Jun 1 2020

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics, Probability and Uncertainty
Applied Mathematics

Keywords

Cross-validation
Geodesic convexity
Marchenko-Pastur distribution
Penalization
Principal component
Spiked covariance matrix

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10.1093/biomet/asz076

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title = "Lassoing eigenvalues",

abstract = "The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.",

keywords = "Cross-validation, Geodesic convexity, Marchenko-Pastur distribution, Penalization, Principal component, Spiked covariance matrix",

author = "Tyler, {David E.} and Mengxi Yi",

note = "Funding Information: We thank Jianhua Huang and Haipeng Shen for providing us with the edited version of the call centre data analysed in this paper. The original dataset was made available to them by Avi Mandelbaum. An R (R Development Core Team, 2020) package to implement the elasso is currently being developed in collaboration with Klaus Nordhausen. Yi was supported in part by the Scientific Research Starting Foundation of the University of International Business and Economics, Beijing. Both authors were supported in part by the U.S. National Science Foundation. Publisher Copyright: {\textcopyright} 2020 Biometrika Trust.",

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doi = "10.1093/biomet/asz076",

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AU - Tyler, David E.

AU - Yi, Mengxi

N1 - Funding Information: We thank Jianhua Huang and Haipeng Shen for providing us with the edited version of the call centre data analysed in this paper. The original dataset was made available to them by Avi Mandelbaum. An R (R Development Core Team, 2020) package to implement the elasso is currently being developed in collaboration with Klaus Nordhausen. Yi was supported in part by the Scientific Research Starting Foundation of the University of International Business and Economics, Beijing. Both authors were supported in part by the U.S. National Science Foundation. Publisher Copyright: © 2020 Biometrika Trust.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

AB - The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

KW - Cross-validation

KW - Geodesic convexity

KW - Marchenko-Pastur distribution

KW - Penalization

KW - Principal component

KW - Spiked covariance matrix

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SP - 397

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JO - Biometrika

JF - Biometrika

IS - 2

ER -

Lassoing eigenvalues

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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