Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation

2019/01/23 by Blanchet, Jose, Si, Nian
#FOS: Mathematics #Optimization and Control (math.OC) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1901.07693

Abstract

In a recent paper, Nguyen, Kuhn, and Esfahani (2018) built a distributionally robust estimator for the precision matrix of the Gaussian distribution. The distributional uncertainty size is a key ingredient in the construction of this estimator. We develop a statistical theory which shows how to optimally choose the uncertainty size to minimize the associated Stein loss. Surprisingly, rather than the expected canonical square-root scaling rate, the optimal uncertainty size scales linearly with the sample size.

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