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Convergence in probability of the Mallows and GCV wavelet and Fourier regularization methods

✍ Scribed by Umberto Amato; Daniela De Canditiis

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
79 KB
Volume
54
Category
Article
ISSN
0167-7152

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✦ Synopsis

Wavelet and Fourier regularization methods are e ective for the nonparametric regression problem. We prove that the loss function evaluated for the regularization parameter chosen through GCV or Mallows criteria is asymptotically equivalent in probability to its minimum over the regularization parameter.

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