Goodness-of-fit Tests for high-dimensional Gaussian linear models
| dc.creator | Verzelen, Nicolas | |
| dc.creator | Villers, Fanny | |
| dc.date | 2007-11-14 | |
| dc.date | 2008-05-23 | |
| dc.date.accessioned | 2026-07-07T09:40:15Z | |
| dc.date.available | 2026-07-07T09:40:15Z | |
| dc.description | 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 propose a new test for testing that $Y$ is independent of $(X_i)_{i\in \mathcal{I}\backslash V}$ conditionally to $(X_i)_{i\in V}$ against the general alternative that it is not. This procedure does not depend on any prior information on the covariance of $X$ or the variance of $Y$ and applies in a high-dimensional setting. It straightforwardly extends to test the neighbourhood of a Gaussian graphical model. The procedure is based on a model of Gaussian regression with random Gaussian covariates. We give non asymptotic properties of the test and we prove that it is rate optimal (up to a possible $\log(n)$ factor) over various classes of alternatives under some additional assumptions. Besides, it allows us to derive non asymptotic minimax rates of testing in this setting. Finally, we carry out a simulation study in order to evaluate the performance of our procedure. | |
| dc.identifier | https://arxiv.org/abs/0711.2119 | |
| dc.identifier | http://arxiv.org/abs/0711.2119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161427 | |
| dc.subject | Statistics Theory | |
| dc.title | Goodness-of-fit Tests for high-dimensional Gaussian linear models | |
| dc.type | text |