publication . Article . Preprint . Other literature type . 2011

Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism

Arias-Castro, Ery; Candès, Emmanuel J.; Plan, Yaniv;
Open Access English
  • Published: 01 Oct 2011 Journal: issn: 0090-5364, Copyright policy
  • Publisher: The Institute of Mathematical Statistics
Abstract
Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have $p$ covariates and that under the alternative, the response only depends upon the order of $p^{1-\alpha}$ of those, $0\le\alpha\le1$. Under moderate sparsity levels, that is, $0\le\alpha\le1/2$, we show that ANOVA is essentially optimal under some conditions on the design. This is no longer the case unde...
Subjects
free text keywords: incoherence, random matrices, Mathematics - Statistics Theory, analysis of variance, 94A13, Statistics - Methodology, minimax detection, 62G20, higher criticism, 62G10, suprema of Gaussian processes, compressive sensing, Detecting a sparse signal
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publication . Article . Preprint . Other literature type . 2011

Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism

Arias-Castro, Ery; Candès, Emmanuel J.; Plan, Yaniv;