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Minimum Covariance Determinant: Spectral Embedding and Subset Size Determination

Abstract Number:

1954

Submission Type:

Contributed Abstract

Contributed Abstract Type:

Paper

Participants:

Qiang Heng (1), Yichi Zhang (2), Kenneth Lange (1)

Institutions:

(1) University of California, Los Angeles, N/A, (2) Duke University, N/A

Co-Author(s):

Yichi Zhang
Duke University

Kenneth Lange
University of California, Los Angeles

First Author:

Qiang Heng
University of California, Los Angeles

Presenting Author:

Qiang Heng
N/A

Abstract Text:

This paper introduces several ideas to the minimum covariance determinant problem for outlier detection and robust estimation of means and covariances. We leverage the principal component transform to achieve dimension reduction, paving the way for improved analyses. Our best subset selection algorithm strategically combines statistical depth and concentration steps. To ascertain the appropriate subset size and number of principal components, we introduce a novel bootstrap procedure that estimates the instability of the best subset algorithm. The parameter combination exhibiting minimal instability proves ideal for the purposes of outlier detection and robust estimation. Rigorous benchmarking against prominent MCD variants showcases our approach's superior capability in outlier detection and computational speed in high dimensions. Application to a fruit spectra data set and a cancer genomics data set illustrates our claims.

Keywords:

Sponsors:

Section on Statistical Computing

Tracks:

Data Science

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