On weighted multivariate sign functions

Subhabrata Majumdar; Snigdhansu Chatterjee

doi:10.1016/j.jmva.2022.105013

On weighted multivariate sign functions

Subhabrata Majumdar, Snigdhansu Chatterjee

Statistics (Twin Cities)

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

Abstract

Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.

Original language	English (US)
Article number	105013
Journal	Journal of Multivariate Analysis
Volume	191
DOIs	https://doi.org/10.1016/j.jmva.2022.105013
State	Published - Sep 2022

Bibliographical note

Funding Information:
We thank the Editor, Associate Editor, and two anonymous referees for their insightful comments that led to improvements in the paper. The research of SC is partially supported by the US National Science Foundation grants 1737918 , 1939916 and 1939956 and a grant from Cisco Systems Inc.

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

Data depth
Multivariate sign
Outlier detection
Principal component analysis
Sufficient dimension reduction

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10.1016/j.jmva.2022.105013

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title = "On weighted multivariate sign functions",

abstract = "Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.",

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author = "Subhabrata Majumdar and Snigdhansu Chatterjee",

note = "Funding Information: We thank the Editor, Associate Editor, and two anonymous referees for their insightful comments that led to improvements in the paper. The research of SC is partially supported by the US National Science Foundation grants 1737918 , 1939916 and 1939956 and a grant from Cisco Systems Inc. Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

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doi = "10.1016/j.jmva.2022.105013",

language = "English (US)",

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AU - Majumdar, Subhabrata

AU - Chatterjee, Snigdhansu

N1 - Funding Information: We thank the Editor, Associate Editor, and two anonymous referees for their insightful comments that led to improvements in the paper. The research of SC is partially supported by the US National Science Foundation grants 1737918 , 1939916 and 1939956 and a grant from Cisco Systems Inc. Publisher Copyright: © 2022 Elsevier Inc.

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N2 - Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.

AB - Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while significantly improving efficiency in estimation and inference compared to unweighted multivariate sign-based methods. Using weighted signs, we demonstrate methods of robust location estimation and robust principal component analysis. We extend the scope of using robust multivariate methods to include robust sufficient dimension reduction and functional outlier detection. Several numerical studies and real data applications demonstrate the efficacy of the proposed methodology.

KW - Data depth

KW - Multivariate sign

KW - Outlier detection

KW - Principal component analysis

KW - Sufficient dimension reduction

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JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

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ER -

On weighted multivariate sign functions

Abstract

Bibliographical note

Keywords

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