Goodness-of-fit Tests for high-dimensional Gaussian linear models

Nicolas Verzelen, Fanny Villers

Let $(Y,(X_i{)}_{i\in \mathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $\mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propos…