Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation

Jose Blanchet; Nian Si

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arXiv · 1901.07693

Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation

Jose Blanchet·Nian Si

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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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Jose Blanchet, Nian Si. 2019-01-23. Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation. https://arxiv.org/abs/1901.07693

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