On the risk estimate of stabilized hard threshold processing when solving inverse statistical problems in models with long-term dependence

Recieved: 05/15/2025

Accepted: 06/19/2025

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

To cite this article

Suhareva N. A., Shestakov O.V. On the risk estimate of stabilized hard threshold processing when solving inverse statistical problems in models with long-term dependence. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2025. N 4, p.68-73 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–4–68–73.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Suhareva N. A. (Lomonosov Moscow State University (MSU))
Shestakov O.V. (Lomonosov Moscow State University (MSU))

Abstract

The paper considers a method of stabilized hard thresholding in the problem of inverting linear homogeneous operators using wavelet decomposition. In a data model with additive Gaussian noise, an analysis of the unbiased estimate of the mean square risk of this method is carried out. Under the assumption of a long-term dependence between noise coefficients, conditions are given under which the unbiased risk estimate is strongly consistent and asymptotically normal.