Multiple testing along a tree
Werner Ehm, Jürgen Kornmeier, and Sven P. Heinrich
Source: Electron. J. Statist. Volume 4
(2010), 461-471.
Abstract
Suitable sequentially rejective multiple test procedures allow to “zoom in" on clusters of relevant variables in high-dimensional regression (Meinshausen [7]), or on regions of interest in some search space (Heinrich et al. [3]; Meinshausen et al. [8]). 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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ejs/1274794929
Digital Object Identifier: doi:10.1214/09-EJS496
Mathematical Reviews number (MathSciNet): MR2657377
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.
Mathematical Reviews (MathSciNet): MR1325392
JSTOR: links.jstor.org
[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.
Mathematical Reviews (MathSciNet): MR538597
[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.
Mathematical Reviews (MathSciNet): MR2524336
Zentralblatt MATH: 05591278
Digital Object Identifier: doi:10.1214/07-AOAS137
Project Euclid: euclid.aoas/1215118518
[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.
Mathematical Reviews (MathSciNet): MR468056
Zentralblatt MATH: 0353.62037
Digital Object Identifier: doi:10.1093/biomet/63.3.655
JSTOR: links.jstor.org
[7] Meinshausen, N. (2008). Hierarchical testing of variable importance., Biometrika 95, 265–278.
Mathematical Reviews (MathSciNet): MR2521583
Zentralblatt MATH: 05563394
Digital Object Identifier: doi:10.1093/biomet/asn007
[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.
[9] Shaffer, J.P. (1986). Modified sequentially rejective multiple test procedures., J. Amer. Statist. Assoc. 81, 826–831.
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