# A Global Homogeneity Test for High-Dimensional Linear Regression

Abstract : This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from estimation uncertainties. Adopting a neighborhood approach, we consider a two-sample linear regression model with random design and propose a procedure to test whether these two regressions are the same. Relying on multiple testing and variable selection strategies, we develop a testing procedure that applies to high-dimensional settings where the number of covariates $p$ is larger than the number of observations $n_1$ and $n_2$ of the two samples. Both type I and type II errors are explicitely controlled from a non-asymptotic perspective and the test is proved to be minimax adaptive to the sparsity. The performances of the test are evaluated on simulated data. Moreover, we illustrate how this procedure can be used to compare genetic networks on Hess \emph{et al} breast cancer microarray dataset.
Keywords :
Type de document :
Pré-publication, Document de travail
2014
Domaine :

https://hal.archives-ouvertes.fr/hal-00851592
Contributeur : Camille Charbonnier <>
Soumis le : lundi 16 juin 2014 - 14:06:47
Dernière modification le : lundi 29 mai 2017 - 14:23:56
Document(s) archivé(s) le : mardi 11 avril 2017 - 07:01:40

### Fichiers

CLR-revised-04-06-14.pdf
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### Identifiants

• HAL Id : hal-00851592, version 2
• ARXIV : 1308.3568

### Citation

Camille Charbonnier, Nicolas Verzelen, Fanny Villers. A Global Homogeneity Test for High-Dimensional Linear Regression. 2014. <hal-00851592v2>

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