Estimating the Proportion of True Null Hypotheses: A Likelihood Approach

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Hualing Zhao
Hualing Zhao
2
Hanfeng Chen
Hanfeng Chen
1 Wuhan University of Technology

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Many estimators for the proportion of the true null hypotheses in a multiple testing problem have been proposed in literature. Motivated from the work on the histogram approach, in this article we propose a new estimator based on the likelihood function with an approximating alternative histogram. AIC is used to select the number of bins for the histogram. Simulation study demonstrates that the new estimator outperforms and substantially improves existing methods including Storey estimators, convex density estimator, and histogram estimator. The new method is applied to a real-life data set of breast cancer.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Hualing Zhao. 2021. \u201cEstimating the Proportion of True Null Hypotheses: A Likelihood Approach\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 21 (GJSFR Volume 21 Issue F5): .

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Accurate evaluation of null hypothesis proportion in research studies.
Issue Cover
GJSFR Volume 21 Issue F5
Pg. 17- 27
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 97K80
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v1.2

Issue date

December 30, 2021

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English

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Many estimators for the proportion of the true null hypotheses in a multiple testing problem have been proposed in literature. Motivated from the work on the histogram approach, in this article we propose a new estimator based on the likelihood function with an approximating alternative histogram. AIC is used to select the number of bins for the histogram. Simulation study demonstrates that the new estimator outperforms and substantially improves existing methods including Storey estimators, convex density estimator, and histogram estimator. The new method is applied to a real-life data set of breast cancer.

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Estimating the Proportion of True Null Hypotheses: A Likelihood Approach

Hualing Zhao
Hualing Zhao Wuhan University of Technology
Hanfeng Chen
Hanfeng Chen

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