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


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).

Journal of Open Source Software