A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric

Olivier Besson (1) , François Vincent (2) , Xavier Gendre (3)

1 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace
2 DEOS - Département Electronique, Optronique et Signal
3 DISC - Département d'Ingénierie des Systèmes Complexes

We consider a Stein's approach to estimate a covariance matrix using regularization of the sample covariance matrix Cholesky factor. We propose a method to estimate accurately the regularization vector which minimizes the risk associated with the recently introduced log-Cholesky metric.

Mots clés: Cholesky factor; Covariance matrix estimation; Regularization; Steins’s estimation

Domaines: Traitement du signal et de l'image [eess.SP]

Olivier Besson, François Vincent, Xavier Gendre. A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric. Statistics and Probability Letters, 2020, 167, pp.1-9. ⟨10.1016/j.spl.2020.108893⟩. ⟨hal-02923042⟩