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B0762
Title: Optimal and adaptive shrinkage estimators for general large covariance and precision matrices Authors:  Xiucai Ding - UC Davis (United States) [presenting]
Abstract: Some recent results are shown on the estimation of high dimensional covariance and precision matrices using Stein's invariant (shrinkage) estimators under various loss functions. We provide the first general analytical formulas for Stein's estimators for various loss functions for both the spiked and non-spiked models. Based on our formulas, we also propose optimal and adaptive estimators for these shrinkers. An algorithm and R package are provided to conduct the calculations. In order to study the asymptotics of our estimators, we establish the asymptotic normality for all the non-outlier eigenvectors and their associated quantum unique ergodicity (QUE) for a potentially spiked model.