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Asymptotic Properties of MSE Estimate for the False Discovery Rate Controlling Procedures in Multiple Hypothesis Testing

Author

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  • Sofia Palionnaya

    (Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, 119991 Moscow, Russia)

  • Oleg Shestakov

    (Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, 119991 Moscow, Russia
    Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Moscow, Russia)

Abstract

Problems with analyzing and processing high-dimensional random vectors arise in a wide variety of areas. Important practical tasks are economical representation, searching for significant features, and removal of insignificant (noise) features. These tasks are fundamentally important for a wide class of practical applications, such as genetic chain analysis, encephalography, spectrography, video and audio processing, and a number of others. Current research in this area includes a wide range of papers devoted to various filtering methods based on the sparse representation of the obtained experimental data and statistical procedures for their processing. One of the most popular approaches to constructing statistical estimates of regularities in experimental data is the procedure of multiple testing of hypotheses about the significance of observations. In this paper, we consider a procedure based on the false discovery rate (FDR) measure that controls the expected percentage of false rejections of the null hypothesis. We analyze the asymptotic properties of the mean-square error estimate for this procedure and prove the statements about the asymptotic normality of this estimate. The obtained results make it possible to construct asymptotic confidence intervals for the mean-square error of the FDR method using only the observed data.

Suggested Citation

  • Sofia Palionnaya & Oleg Shestakov, 2020. "Asymptotic Properties of MSE Estimate for the False Discovery Rate Controlling Procedures in Multiple Hypothesis Testing," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1913-:d:438581
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    References listed on IDEAS

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    1. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
    2. Yoav Benjamini & Daniel Yekutieli, 2005. "False Discovery Rate-Adjusted Multiple Confidence Intervals for Selected Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 71-81, March.
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