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Abstract:
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In this presentation, I will focus on estimating the noise covariance for multi-task high-dimensional linear models. Building upon second-order Stein formula, we propose a novel noise covariance estimator and establish its convergence rate. Under certain conditions, we show that the proposed estimator attains the optimal rate of convergence as the ``oracle" estimator which assumes the coefficient matrix of the multi-task linear models are known. Extensive simulation studies are carried out to illustrate the superior performance of the proposed method over existing methods.
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