Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals for General Multivariate Factorial Designs




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In many scientific fields, the most frequently used experimental or observational study designs rely on multivariate layouts. Such designs can have more than two possibly correlated response variables observed on each experimental unit and should allow comparisons across different treatment groups. In this dissertation, we make three contributions to modeling and analysis of multivariate data using purely nonparametric inference methods that neither assume any specific data distribution nor identical covariance matrices across the treatment groups. The hypotheses are formulated in terms of purely nonparametric treatment effects. In the first contribution, we derive rank-based multiple contrast tests 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 tests, the corresponding simultaneous confidence interval does not include the null, i.e., the hypothetical value of no treatment effect. The modification of the test statistics to their finite sample distributions is also presented. In the second contribution, we develop a wild bootstrap method as an alternative to approximate the limiting distribution of the multiple tests for small sample sizes. The third contribution is the extension of the rank-based multiple test procedures to factorial multivariate repeated measures designs. Moreover, the finite sample performance of the asymptotic tests is evaluated using a wild bootstrap version of the multiple tests. The small-sample performances of all test procedures are examined in extensive simulation studies and the results show that the proposed procedures achieve accurate control of the multiple type-I error rate and comparable power to existing nonparametric global test procedures. Real data examples illustrate the application of the proposed tests.



Multivariate analysis -- Data processing, Nonparametric statistics, Confidence intervals