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Abstract <p>We consider an approach to solving the problem of noise removal in a large array of sparse data under conditions of weak dependence, based on the method of controlling the average proportion of false hypothesis rejections. The statements about the strong consistency and asymptotic normality of the SURE estimate are proved. The rates of convergence of the estimate distribution to the normal law are also obtained.</p>

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Asymptotic Results for the Mean-Square Risk when Using Multiple Hypothesis Testing Methods for Weakly Dependent Observations

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • M. O. Vorontsov,
  • O. V. Shestakov

摘要

Abstract

We consider an approach to solving the problem of noise removal in a large array of sparse data under conditions of weak dependence, based on the method of controlling the average proportion of false hypothesis rejections. The statements about the strong consistency and asymptotic normality of the SURE estimate are proved. The rates of convergence of the estimate distribution to the normal law are also obtained.