Minimum Covariance Determinant: Spectral Embedding and Subset Size Determination

This paper introduces several enhancements to the minimum covariance determinant method of outlier detection and robust estimation of means and covariances. We leverage the principal component transform to achieve dimension reduction and ultimately better 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 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 statistical performance and computational speed in high dimensions. Application to a fruit spectra data set and a cancer genomics data set illustrates our claims.