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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Joint mirror procedure: controlling false discovery rate for identifying simultaneous signals.

Linsui Deng1,2, Kejun He2, Xianyang Zhang3

  • 1School of Data Science, The Chinese University of Hong Kong, Shenzhen 518172, China.

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|December 13, 2024
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Summary

This study introduces the joint mirror (JM) procedure for testing multiple hypotheses simultaneously. The JM procedure effectively controls the composite false discovery rate (cFDR) and enhances statistical power in various scenarios.

Keywords:
composite nullmediation analysismultiple hypothesis testingreplicability analysis

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Area of Science:

  • Statistical methodology
  • Hypothesis testing
  • Data analysis

Background:

  • Identifying specific features often requires testing multiple hypotheses for joint statistical significance.
  • Applications include mediation and replicability analyses, which examine multiple effects or signals simultaneously.

Purpose of the Study:

  • To present a novel joint mirror (JM) procedure for detecting features of interest through joint hypothesis testing.
  • To control the false discovery rate (FDR) and introduce a more stringent composite FDR (cFDR) measure.
  • To enhance statistical power in detecting significant features.

Main Methods:

  • The JM procedure uses an iterative shrinkage approach to control the false discovery proportion.
  • A leave-one-out technique is employed to prove cFDR control in finite samples.
  • An efficient algorithm is proposed for implementing the JM procedure, accommodating partial ordering.

Main Results:

  • The JM procedure effectively controls the composite FDR (cFDR) in finite samples.
  • Simulations demonstrate enhanced statistical power across diverse scenarios, including dependent test statistics.
  • The method proves useful in real-world mediation and replicability analyses.

Conclusions:

  • The joint mirror (JM) procedure offers a robust method for joint hypothesis testing.
  • It provides effective FDR control and improved statistical power compared to existing methods.
  • The JM procedure is applicable to complex real-world data analyses in fields like biostatistics and genetics.