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

Umberto Amato and Daniela De Canditiis

Statistics & Probability Letters, 2001, vol. 54, issue 3, 325-329

Abstract: Wavelet and Fourier regularization methods are effective 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.

Keywords: Nonparametric; regression; Wavelet; series; Fourier; series; GCV; Mallows; criterion; Convergence (search for similar items in EconPapers)
Date: 2001
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