Abstract

Procedures for multiple hypothesis testing are widely used in analyzing data arrays. Transformation is done first, producing an economic (sparse) array representation. Data is then processed by testing hypotheses of data significance and using inverse transformation. Noise suppression and/or data compression are the main goals of this approach. Such techniques are used in the theory of communication, astronomy, physics, biology, medicine, and a number of areas of practical interest. Risk (error) analysis for such procedures is one of the most important challenges, as it is essential for estimating the quality of applied techniques and equipment. In this work, we consider the Benjamini-Hochberg algorithm of multiple hypothesis testing in selecting the FDR threshold. The strong consistency of the risk estimator is also proved for the case of sparse data.

中文翻译：

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具有FDR阈值的多重假设检验中风险估计器的强一致性

摘要

多种假设检验的过程广泛用于分析数据数组。首先进行转换，产生经济的（稀疏）数组表示形式。然后，通过测试数据重要性假设并使用逆变换来处理数据。噪声抑制和/或数据压缩是此方法的主要目标。此类技术被用于通信理论，天文学，物理学，生物学，医学以及许多实际感兴趣的领域。此类程序的风险（错误）分析是最重要的挑战之一，因为这对于评估应用技术和设备的质量至关重要。在这项工作中，我们在选择FDR阈值时考虑了多个假设检验的Benjamini-Hochberg算法。