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Constructing confidence intervals for selected parameters

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  • Haibing Zhao
  • Xinping Cui

Abstract

In large‐scale problems, it is common practice to select important parameters by a procedure such as the Benjamini and Hochberg procedure and construct confidence intervals (CIs) for further investigation while the false coverage‐statement rate (FCR) for the CIs is controlled at a desired level. Although the well‐known BY CIs control the FCR, they are uniformly inflated. In this paper, we propose two methods to construct shorter selective CIs. The first method produces shorter CIs by allowing a reduced number of selective CIs. The second method produces shorter CIs by allowing a prefixed proportion of CIs containing the values of uninteresting parameters. We theoretically prove that the proposed CIs are uniformly shorter than BY CIs and control the FCR asymptotically for independent data. Numerical results confirm our theoretical results and show that the proposed CIs still work for correlated data. We illustrate the advantage of the proposed procedures by analyzing the microarray data from a HIV study.

Suggested Citation

  • Haibing Zhao & Xinping Cui, 2020. "Constructing confidence intervals for selected parameters," Biometrics, The International Biometric Society, vol. 76(4), pages 1098-1108, December.
    • Handle: RePEc:bla:biomet:v:76:y:2020:i:4:p:1098-1108
    DOI: 10.1111/biom.13222
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    References listed on IDEAS

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    Cited by:

    1. Jelle J Goeman & Aldo Solari, 2024. "On selection and conditioning in multiple testing and selective inference," Biometrika, Biometrika Trust, vol. 111(2), pages 393-416.

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