Electronic Journal of Statistics

Rank-based multiple test procedures and simultaneous confidence intervals

Frank Konietschke, Ludwig A. Hothorn, and Edgar Brunner

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Abstract

We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses (e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.

Article information

Source
Electron. J. Statist. Volume 6 (2012), 738-759.

Dates
First available in Project Euclid: 3 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1336049813

Digital Object Identifier
doi:10.1214/12-EJS691

Mathematical Reviews number (MathSciNet)
MR2988427

Zentralblatt MATH identifier
1334.62083

Keywords
Rank statistics multiple comparisons nonparametric Behrens-Fisher problem

Citation

Konietschke, Frank; Hothorn, Ludwig A.; Brunner, Edgar. Rank-based multiple test procedures and simultaneous confidence intervals. Electron. J. Statist. 6 (2012), 738--759. doi:10.1214/12-EJS691. https://projecteuclid.org/euclid.ejs/1336049813.


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