cvCovEst: Cross-validated covariance matrix estimator selection and evaluation in R

Abstract

Covariance matrices play fundamental roles in myriad statistical procedures. When the observations in a dataset far outnumber the features, asymptotic theory and empirical evidence have demonstrated the sample covariance matrix to be the optimal estimator of this parameter. This assertion does not hold when the number of observations is commensurate with or smaller than the number of features. Consequently, statisticians have derived many novel covariance matrix estimators for the high-dimensional regime, often relying on additional assumptions about the parameter's structural characteristics (e.g., sparsity). While these estimators have greatly improved the ability to estimate covariance matrices in high-dimensional settings, objectively selecting the best estimator from among the many possible candidates remains a largely unaddressed challenge. The cvCovEst package addresses this methodological gap through its implementation of a cross-validated framework for covariance matrix estimator selection. This data-adaptive procedure's selections are asymptotically optimal under minimal assumptions -in fact, they are equivalent to the selections that would be made if given full knowledge of the true data-generating processes (i.e., an oracle selector) (van der Laan & Dudoit, 2003).

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

“…As the empirical correlation matrix is known to be a non accurate estimator of when p is larger than n , a new estimator has to be used. Thus, for estimating we adopted a cross-validation based method designed by [ 5 ] and implemented in the cvCovEst R package [ 6 ]. This method chooses the estimator having the smallest estimation error among several compared methods (sample correlation matrix, POET [ 11 ] and Tapering [ 7 ] as examples).…”

A Flexible Approach for Predictive Biomarker Discovery

“…The biomarker covariance matrix, Σ, is the estimated gene expression correlation matrix of the 500 most variable genes taken from the tumours of patients with metastatic or recurrent colorectal cancer [Watanabe et al, 2011]. These genes were first clustered using hierarchical clustering based on their Euclidean distance with complete linkage, and the correlation matrix was then estimated using the cross-validated estimation procedure of Boileau et al [2021a] implemented in the cvCovEst R package [Boileau et al, 2021b, R Core Team, 2022, relying on the banding and tapering estimators of Bickel and Levina [2008] and Cai et al [2010], respectively. The gene expression data has been made available by the Bioconductor [Huber et al, 2015] experiment package curatedCRCdata [Parsana et al, 2021].…”