A. A. Eroshenko, “Consistency of risk estimates for wavelet-vaguelette and vaguelette-wavelet decompositions of signal function in the model of data with correlated noise”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2015, Issue 1,Pages <nobr>103

System Analysis, Control and Data Processing

Consistency of risk estimates for wavelet-vaguelette and vaguelette-wavelet decompositions of signal function in the model of data with correlated noise

A. A. Eroshenko

Lomonosov Moscow State University, Moscow

Abstract: In the present paper we consider the problem of estimating function after applying linear homogeneous operator in the model of data with correlated noise. We study asymptotical properties of risk estimates of thresholding methods for wavelet-vaguelette and vaguelette-wavelet decompositions of a signal. We give the conditions under which the unbiased risk estimates are consistent.

Keywords: wavelets, linear homogeneous operator, thresholding, unbiased risk estimate, correlated noise, consistency.

UDC: 519.22, 517.521, 53.088

Received: 08.10.2014
Revised: 20.10.2014