Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices

23 Dec 2019Jaouad Mourtada

The first part of this paper is devoted to the decision-theoretic analysis of random-design linear prediction. It is known that, under boundedness constraints on the response (and thus on regression coefficients), the minimax excess risk scales, up to constants, as $\sigma^2 d / n$ in dimension $d$ with $n$ samples and noise $\sigma^2$... (read more)

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