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2018 Confidence intervals for the means of the selected populations
Claudio Fuentes, George Casella, Martin T. Wells
Electron. J. Statist. 12(1): 58-79 (2018). DOI: 10.1214/17-EJS1374

Abstract

Consider an experiment in which $p$ independent populations $\pi_{i}$ with corresponding unknown means $\theta_{i}$ are available, and suppose that for every $1\leq i\leq p$, we can obtain a sample $X_{i1},\ldots,X_{in}$ from $\pi_{i}$. In this context, researchers are sometimes interested in selecting the populations that yield the largest sample means as a result of the experiment, and then estimate the corresponding population means $\theta_{i}$. In this paper, we present a frequentist approach to the problem and discuss how to construct simultaneous confidence intervals for the means of the $k$ selected populations, assuming that the populations $\pi_{i}$ are independent and normally distributed with a common variance $\sigma^{2}$. The method, based on the minimization of the coverage probability, obtains confidence intervals that attain the nominal coverage probability for any $p$ and $k$, taking into account the selection procedure.

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Claudio Fuentes. George Casella. Martin T. Wells. "Confidence intervals for the means of the selected populations." Electron. J. Statist. 12 (1) 58 - 79, 2018. https://doi.org/10.1214/17-EJS1374

Information

Received: 1 February 2016; Published: 2018
First available in Project Euclid: 5 January 2018

zbMATH: 1384.62058
MathSciNet: MR3743737
Digital Object Identifier: 10.1214/17-EJS1374

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Vol.12 • No. 1 • 2018
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