Comments on: Augmenting the bootstrap to analyze high dimensional genomic data Connections between the augmented bootstrap and the shrinkage covariance estimator

In their enlightening and stimulating paper Svitlana Tyekucheva and Francesca Chiaromonte propose an “augmented bootstrap” (AB) approach to estimate covariance structure in high-dimensional data. They show that the AB estimator performs well in a catalog of examples. Moreover, according to the authors no assumption of a sparsity rationale is made. This is in contrast to a competing and computationally less expensive Stein-type “shrinkage” (SH) approach. In my comments I address the relationship between the AB and the SH estimators. Perhaps surprisingly, it turns out that there is a very close connection between the two approaches. This leaves questions concerning their relative performance in the examples presented in the paper, an issue which I also discuss below.