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Conditionally unbiased estimation in the normal setting with unknown variances

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  • David S. Robertson
  • Ekkehard Glimm

Abstract

To efficiently and completely correct for selection bias in adaptive two-stage trials, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been derived for trial designs with normally distributed data. However, a common assumption is that the variances are known exactly, which is unlikely to be the case in practice. We extend the work of Cohen and Sackrowitz (Statistics & Probability Letters, 8(3):273-278, 1989), who proposed an UMVCUE for the best performing candidate in the normal setting with a common unknown variance. Our extension allows for multiple selected candidates, as well as unequal stage one and two sample sizes.

Suggested Citation

  • David S. Robertson & Ekkehard Glimm, 2019. "Conditionally unbiased estimation in the normal setting with unknown variances," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(3), pages 616-627, February.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:3:p:616-627
    DOI: 10.1080/03610926.2017.1417429
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