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Abstract <p>This work considers a means of stabilized hard thresholding for inverting linear homogeneous operators using wavelet decomposition. The unbiased mean squared risk estimate for this procedure is analyzed using a data model with additive Gaussian noise. Assuming there is a long-range dependence among noise coefficients, conditions are given that ensure strong consistency and asymptotic normality of the unbiased risk estimator.</p>

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Estimating the Risk of Stabilized Hard Thresholding for Inverse Statistical Problems in Models with Long-Range Dependences

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • N. A. Sukhareva,
  • O. V. Shestakov

摘要

Abstract

This work considers a means of stabilized hard thresholding for inverting linear homogeneous operators using wavelet decomposition. The unbiased mean squared risk estimate for this procedure is analyzed using a data model with additive Gaussian noise. Assuming there is a long-range dependence among noise coefficients, conditions are given that ensure strong consistency and asymptotic normality of the unbiased risk estimator.