Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism
نویسندگان
چکیده
منابع مشابه
Global Testing under Sparse Alternatives: ANOVA, Multiple Comparisons and the Higher Criticism
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 ...
متن کاملGLOBAL TESTING UNDER SPARSE ALTERNATIVES: ANOVA, MULTIPLE COMPARISONS AND THE HIGHER CRITICISM By
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 ...
متن کاملTo “ Global Testing under Sparse Alternatives : Anova , Multiple Comparisons and the Higher Criticism ”
We prove the results stated in the main paper. We start by providing a brief summary of the notations used in the paper. Set [p] = {1, . . . , p} and for a subset J ⊂ [p], let |J | be its cardinality. Bold upper (resp. lower) case letters denote matrices (resp. vectors), and the same letter not bold represents its coefficients, e.g. aj denotes the jth entry of a. For an n × p matrix A with colu...
متن کاملGlobal Testing under Sparse Alternatives: Anova, Multiple Comparisons and the Higher Criticism1 by Ery Arias-castro,
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 ...
متن کاملGlobal Testing Against Sparse Alternatives under Ising Models
In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the strength and sparsity of a signal determines its detectability under various notions of dependence. The profound impact of dependence is best illu...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2011
ISSN: 0090-5364
DOI: 10.1214/11-aos910