Conditionally unbiased estimation in the normal setting with unknown variances

• Published in: Communications in statistics. Theory and methods Vol. 48; no. 3; pp. 616 - 627
• Main Authors: Robertson, David S., Glimm, Ekkehard
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 01.02.2019; Taylor & Francis Ltd
• Subjects: 62-07; Original; Selection bias; Two-stage sample; Uniformly minimum variance conditionally unbiased estimation; Variance; 62-07; Selection bias; Two-stage sample; Uniformly minimum variance conditionally unbiased estimation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2017.1417429

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.