Quantile-Function Based Null Distribution in Resampling Based Multiple Testing
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Mark J. van der Laan
Simultaneously testing a collection of null hypotheses about a data generating distribution based on a sample of independent and identically distributed observations is a fundamental and important statistical problem involving many applications. Methods based on marginal null distributions (i.e., marginal p-values) are attractive since the marginal p-values can be based on a user supplied choice of marginal null distributions and they are computationally trivial, but they, by necessity, are known to either be conservative or to rely on assumptions about the dependence structure between the test-statistics. Re-sampling based multiple testing (Westfall and Young, 1993) involves sampling from a joint null distribution of the test-statistics, and controlling (possibly in a, for example, step-down fashion) the user supplied type-I error rate under this joint null distribution for the test-statistics. A generally asymptotically valid null distribution avoiding the need for the subset pivotality condition for the vector of test-statistics was proposed in Pollard, van der Laan (2003) for null hypotheses about general real valued parameters. This null distribution was generalized in Dudoit, vanderLaan, Pollard (2004) to general null hypotheses and test-statistics. In ongoing recent work van der Laan, Hubbard (2005), we propose a new generally asymptotically valid null distribution for the test-statistics and a corresponding bootstrap estimate, whose marginal distributions are user supplied, and can thus be set equal to the (most powerful) marginal null distributions one would use in univariate testing to obtain a p-value. Previous proposed null distributions either relied on a restrictive subset pivotality condition (Westfall and Young) or did not guarantee this latter property (Dudoit, vanderLaan, Pollard, 2004). It is argued and illustrated that the resulting new re-sampling based multiple testing methods provide more accurate control of the wished Type-I error in finite samples and are more powerful. We establish formal results and investigate the practical performance of this methodology in a simulation and data analysis.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Articles in the same Issue
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- Low-Order Conditional Independence Graphs for Inferring Genetic Networks
- A Generalized Clustering Problem, with Application to DNA Microarrays
- A Bayes Regression Approach to Array-CGH Data
- Statistical Selection of Maintenance Genes for Normalization of Gene Expressions
- Predicting the Strongest Domain-Domain Contact in Interacting Protein Pairs
- Dimension Reduction for Classification with Gene Expression Microarray Data
- A New Type of Stochastic Dependence Revealed in Gene Expression Data
- A New Order Estimator for Fixed and Variable Length Markov Models with Applications to DNA Sequence Similarity
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- A Heuristic Bayesian Method for Segmenting DNA Sequence Alignments and Detecting Evidence for Recombination and Gene Conversion
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- An Improved Nonparametric Approach for Detecting Differentially Expressed Genes with Replicated Microarray Data
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- Treating Expression Levels of Different Genes as a Sample in Microarray Data Analysis: Is it Worth a Risk?
- Reader's Reaction
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