A global homogeneity test for high-dimensional linear regression

This paper is motivated by the comparison of genetic networks inferred from high-dimensional datasets originating from high-throughput Omics technologies. 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 explicitly 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 et al. breast cancer microarray dataset