zbMATH — the first resource for mathematics

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.

62G10 Nonparametric hypothesis testing
62J15 Paired and multiple comparisons; multiple testing
62L99 Sequential statistical methods
Full Text: DOI Euclid
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.