Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation
Statistics Theory
2019-10-11 v3 Optimization and Control
Statistics Theory
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.
Cite
@article{arxiv.1901.07693,
title = {Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation},
author = {Jose Blanchet and Nian Si},
journal= {arXiv preprint arXiv:1901.07693},
year = {2019}
}