Journées de Probabilités 2024

Sample correlation matrices in high-dimensional framework

12 juin 2024, 11:45

30m

Salle de Conférénces (Institut de mathématiques de Bordeaux)

Orateur

Marguerite Zani (Université d'Orléans)

Description

We study the $\tau$-coherence of a $(n\times p)$-observation matrix in a Gaussian framework where both $n$ and $p$ are large and $p>>n$.
The $\tau$-coherence is defined as the largest magnitude, outside a band of size $\tau =\tau (n)$, of the empirical correlation coefficients associated to the observations.
Using the Chen-Stein method we show the convergence of the normalized coherence towards a Gumbel distribution. We broaden previous results by considering a 3-regime band structure for the off diagonal covariance matrix. We introduce an hypothese test for the covariance structure where we study the behaviour under some identifiable alternative.