Abstract
We consider the estimation problem for an unknown vector β ź Rp in a linear model Y = Xβ + źź, where ź ź Rn is a standard discrete white Gaussian noise and X is a known n × p matrix with n ź 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 βź(Y) = Hź(XTX) βź(Y), ź ź R+, where βź(Y) is the maximum likelihood estimate for β and {Hź(·): R+ ź [0, 1], ź ź R+} is a given ordered family of functions indexed by a regularization parameter ź. The final estimate for β is constructed as a convex combination (in ź) of the estimates βź(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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
