Data-adaptive statistics for multiple hypothesis testing in high-dimensional settings

Abstract

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands of null hypotheses. For high-dimensional multivariate distributions, these hypotheses may concern a wide range of parameters, with complex and unknown dependence structures among variables. In analyzing such hypothesis testing procedures, gains in efficiency and power can be achieved by performing variable reduction on the set of hypotheses prior to testing. We present an approach using data-adaptive multiple testing that applies data mining techniques to screen the full set of covariates on equally sized partitions of the sample via cross-validation. This generalized screening procedure is used to create average ranks for covariates, which are then used to generate a reduced (sub)set of hypotheses.

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