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Multiple testing along a tree. (English) Zbl 1329.62212
Summary: Suitable sequentially rejective multiple test procedures allow to “zoom in” on clusters of relevant variables in high-dimensional regression [N. Meinshausen, Biometrika 95, No. 2, 265–278 (2008; Zbl 1437.62557)], or on regions of interest in some search space [the third author et al., “Conquer and divide: a novel approach to spatiotemporal significance testing that accounts for alpha error inflation”, NeuroImage 41, Suppl. 1, S159 (2008); N. Meinshausen et al., Ann. Appl. Stat. 3, No. 1, 38–60 (2009; Zbl 1161.62087)]. As a common framework for these schemes we propose to consider multiple testing along a tree of hypotheses together with a “keep rejecting until first acceptance” rule. Particular topics addressed in this note are control of the familywise error, and some variants and basic properties of the procedure.

MSC:
62G10 Nonparametric hypothesis testing
62J15 Paired and multiple comparisons; multiple testing
62L99 Sequential statistical methods
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References:
[1] Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing., J. R. Statist. Soc. B 57 , 289-300. · Zbl 0809.62014
[2] Goeman, J.J. and Mansmann, U. (2008). Multiple testing on the directed acyclic graph of gene ontology., Bioinformatics 24 , 537-544.
[3] Heinrich, S.P., Bach, M. and Kornmeier, J. (2008). Conquer and Divide: A novel approach to spatiotemporal significance testing that accounts for alpha error inflation., Neuroimage 41 Suppl. 1, p. S159.
[4] Holm, S. (1979). A simple sequentially rejective multiple test procedure., Scand. J. Statist. 6 , 65-70. · Zbl 0402.62058
[5] Lee, A.B., Nadler, B. and Wasserman, L. (2009). Treelets-An adaptive multi-scale basis for sparse unordered data., Ann. Appl. Statist. 2 , 435-471. · Zbl 1400.62274
[6] Marcus, R., Peritz, E. and Gabriel, K.R. (1976). On closed testing procedures with special reference to ordered analysis of variance., Biometrika 63 , 655-660. · Zbl 0353.62037
[7] Meinshausen, N. (2008). Hierarchical testing of variable importance., Biometrika 95 , 265-278. · Zbl 1437.62557
[8] Meinshausen, N., Bickel, P. and Rice, J. (2009). Efficient blind search: Optimal power of detection under computational cost constraints., Ann. Appl. Statist. 3 , 38-60. · Zbl 1161.62087
[9] Shaffer, J.P. (1986). Modified sequentially rejective multiple test procedures., J. Amer. Statist. Assoc. 81 , 826-831. · Zbl 0603.62087
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