Title: Nonasymptotic estimation and support recovery for high dimensional sparse covariance matrices,
Abstract: We propose a general framework for nonasymptotic covariance matrix estimation
making use of concentration inequality-based confidence sets. We specify this
framework for the estimation of large sparse covariance matrices through
incorporation of past thresholding estimators with key emphasis on support
recovery. This technique goes beyond past results for thresholding estimators
by allowing for a wide range of distributional assumptions beyond merely
sub-Gaussian tails. This methodology can furthermore be adapted to a wide range
of other estimators and settings. The usage of nonasymptotic dimension-free
confidence sets yields good theoretical performance. Through extensive
simulations, it is demonstrated to have superior performance when compared with
other such methods. In the context of support recovery, we are able to specify
a false positive rate and optimize to maximize the true recoveries.