On asymptotic normality in estimation after a group sequential trial

We prove that in many realistic cases, the ordinary sample mean after a group sequential trial is asymptotically normal if the maximal number of observations increases. We derive that it is often safe to use naive confidence intervals for the mean of the collected observations, based on the ordinary...

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Bibliographic Details
Published inSequential analysis Vol. 39; no. 4; pp. 443 - 466
Main Authors Berckmoes, Ben, Ivanova, Anna, Molenberghs, Geert
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.10.2020
Taylor & Francis Ltd
Subjects
Asymptotic normality
Asymptotic properties
confidence interval
Confidence intervals
group sequential trial
Normality
sample mean
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ISSN0747-4946
1532-4176
DOI10.1080/07474946.2020.1826784

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Summary:We prove that in many realistic cases, the ordinary sample mean after a group sequential trial is asymptotically normal if the maximal number of observations increases. We derive that it is often safe to use naive confidence intervals for the mean of the collected observations, based on the ordinary sample mean. Our theoretical findings are confirmed by a simulation study.
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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2020.1826784