Comments on: Augmenting the bootstrap to analyze high dimensional genomic data: Connections to the ridge regularized covariance estimator with bagging

摘要

In a timely and stimulating paper. Tyekucheva and Chiaromonte propose an augmented bootstrap (AB) procedure for estimating inverse covariance matrices within the "large p, small n" paradigm. As authors elaborate in detail, such an estimation problem frequently arises in various areas of genomic research. It is our pleasure to discuss this paper and connect it to a related idea of regularized estimation of covariance matrices motivated by ridge regression (Hoerl and Kennard 1970). Let X_(1),..., X_(n) denote a random sample of X E R~(p) with probability distribution function F. Let F_(n)~(j) (h, (tau)~(2)) denote the empirical distribution of jth nonparametric bootstrap sample of size h with a noising parameter of (tau)~(2) >= 0.