Nonparametric multiple test procedures with data-driven order of hypotheses and with weighted hypotheses

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• 作者：Kropf ; Siegfried ; Lä ; uter ; Jü ; rgen ; Eszlinger ; Markus ; Krohn ; Knut ; Paschke ; Ralf
• 关键词：primary 62G10 ; secondary 62G30 ; 62P10 ; 62J15 ; Multiple tests ; Ordered hypotheses ; Nonparametric tests ; Rank statistics ; Order statistics
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2004
• 出版时间：October, 2004
• 年：2004
• 卷：125
• 期：1-2
• 页码：31-47
• 全文大小：291 K

文摘

Recently, Kropf (Shaker Verlag, Aachen, 2000) and Kropf and Läuter (Biometrial J. 44(7) 2002 789) proposed a procedure for testing separate hypotheses concerning the single variables of a multivariate normal population with strong control of the familywise type I error. The procedure is particularly focussed on situations where all variables have approximately equal variances. It establishes a suitable data-driven order of hypotheses and carries out unadjusted tests in that order until the first nonsignificant result. This proposal has been generalised by Westfall et al. (In: Benjamini, Y., Bretz, F., Sarkar, S.K. (Eds.), Recent developments in multiple comparison procedures, IMS Lecture Notes and Monograph Series, IMS, Haywood CA, 2004) in a weighted Bonferroni–Holm procedure that can be tuned with a free parameter η and involves the above procedure as limiting case for η→∞. Here, a nonparametric counterpart is given. Whereas the original parametric procedures utilise properties of spherically distributed matrices to maintain the exact type I error despite the data-dependent sorting or weighting of the variables, the nonparametric procedure exploits the independence of rank and order statistics under the null hypothesis to arrange the variables in a suitable order for unadjusted sequential testing or to weight the variables. Again, the procedures are sensible if the variables have a similar variance. The procedures are demonstrated with data from gene-expression studies in hot or cold thyroid nodules using Affymetrix GeneChips. Furthermore, simulation results are shown to consider the power under various conditions.