On risk concentration for convex combinations of linear estimators

On risk concentration for convex combinations of linear estimators We consider the estimation problem for an unknown vector β ∈ Rp in a linear model Y = Xβ + σξ, where ξ ∈ Rn is a standard discrete white Gaussian noise and X is a known n × p matrix with n ≥ p. It is assumed that p is large and X is an ill-conditioned matrix. To estimate β in this situation, we use a family of spectral regularizations of the maximum likelihood method βα(Y) = H α(X T X) β ◦(Y), α ∈ R+, where β ◦(Y) is the maximum likelihood estimate for β and {H α(·): R+ → [0, 1], α ∈ R+} is a given ordered family of functions indexed by a regularization parameter α. The final estimate for β is constructed as a convex combination (in α) of the estimates βα(Y) with weights chosen based on the observations Y. We present inequalities for large deviations of the norm of the prediction error of this method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On risk concentration for convex combinations of linear estimators

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Pleiades Publishing
Copyright © 2016 by Pleiades Publishing, Inc.
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
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