Open Access
September, 1984 Constrained Simultaneous Confidence Intervals for Multiple Comparisons with the Best
Jason C. Hsu
Ann. Statist. 12(3): 1136-1144 (September, 1984). DOI: 10.1214/aos/1176346732

Abstract

For comparing $k$ treatment effects $\theta_1, \theta_2, \cdots \theta_k$, often the parameters of primary interest are $\theta_i - \max_{j\neq i}\theta_j, i = 1, \cdots, k$. In this article, we develop constrained $100P^\ast{\tt\%}$ two-sided simultaneous confidence intervals for $\theta_i - \max_{j \neq i} \theta_j$ which we refer to as (constrained) MCB intervals. It turns out that the lower bounds of the intervals imply Indifference Zone selection inference, and the upper bounds of these intervals imply Subset Selection inference, each given at the same confidence level $100P^\ast{\tt\%}$ as MCB. We also extend our method to give $100P^\ast{\tt\%}$ simultaneous confidence intervals for $\theta_i - \theta^{(i)}_{(k-t)}, i = 1, \cdots, k$, where $\theta^{(i)}_{(k-t)}$ is the $t$th largest among the $\theta$'s excluding $\theta_i$.

Citation

Download Citation

Jason C. Hsu. "Constrained Simultaneous Confidence Intervals for Multiple Comparisons with the Best." Ann. Statist. 12 (3) 1136 - 1144, September, 1984. https://doi.org/10.1214/aos/1176346732

Information

Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0557.62023
MathSciNet: MR751303
Digital Object Identifier: 10.1214/aos/1176346732

Subjects:
Primary: 62F07
Secondary: 62J15

Keywords: best treatment , Multiple comparisons , simultaneous confidence intervals

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • September, 1984
Back to Top