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Simultaneous Confidence Regions and Weighted Hypotheses on Parameter Arrays

Author

Listed:
  • Yehan Ma

    (Bowling Green State University)

  • Arthur B. Yeh

    (Bowling Green State University)

  • John T. Chen

    (Bowling Green State University)

Abstract

Testing weighted hypotheses simultaneously for a parameter vector has been actively studied in the literature, where the weights encompass information on the importance of the parameters. However, in recent applications of big data analytics for multiple testing on n hypotheses, we are often confronted with the problem of simultaneous inference on a parameter matrix, not a parameter vector. For instance, in the evaluation of overall system reliability, when each subsystem contains k multiple components, the control of global confidence level for the evaluation on system reliability necessitates simultaneous inference on all related parameters in the array of a $$k\times n$$ k × n matrix, where weights are assigned on the basis of the subsystem workloads. So far as we know, there is no publication addressing weighted confidence sets for a parameter matrix. In this paper, we propose a confidence algorithm that generates confidence regions for simultaneous estimation on the parameter array. The new method utilizes a random partition in conjunction with weight assignments to justify for multiplicity. After theoretical derivations, we present simulation studies that cast new lights on intrinsic relationships among coverage probabilities, power performance, and hypothesis weights for multivariate simultaneous confidence sets. For illustration purposes, the new method is applied to analyze factors impacting the taste of red and white wine in a recent study.

Suggested Citation

  • Yehan Ma & Arthur B. Yeh & John T. Chen, 2023. "Simultaneous Confidence Regions and Weighted Hypotheses on Parameter Arrays," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-18, June.
  • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10030-5
    DOI: 10.1007/s11009-023-10030-5
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    References listed on IDEAS

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    1. Oda, Ryoya & Suzuki, Yuya & Yanagihara, Hirokazu & Fujikoshi, Yasunori, 2020. "A consistent variable selection method in high-dimensional canonical discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    2. Lu Wang & Andrea Rotnitzky & Xihong Lin & Randall E. Millikan & Peter F. Thall, 2012. "Evaluation of Viable Dynamic Treatment Regimes in a Sequentially Randomized Trial of Advanced Prostate Cancer," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 493-508, June.
    3. Yang Yu & John T. Chen & Arthur B. Yeh, 2022. "Weighted step-down confidence procedures with applications to gene expression data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(8), pages 2343-2356, April.
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