Comparison of sliced inverse regression approaches for underdetermined cases

Raphaël Coudret (1, 2, 3) , Benoit Liquet (4) , Jerôme Saracco (2, 1, 5)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 EPOC - Environnements et Paléoenvironnements OCéaniques
4 Epidémiologie et Biostatistique [Bordeaux]
5 ENSC - Ecole Nationale Supérieure de Cognitique

Among methods to analyze high-dimensional data, the sliced inverse regression (SIR) is of particular interest for non-linear relations between the dependent variable and some indices of the covariate. When the dimension of the covariate is greater than the number of observations, classical versions of SIR cannot be applied. Various upgrades were then proposed to tackle this issue such as RSIR and SR-SIR, to estimate the parameters of the underlying model and to select variables of interest. In this paper, we introduce two new estimation methods respectively based on the QZ algorithm and on the Moore-Penrose pseudo-inverse. We also describe a new selection procedure of the most relevant components of the covariate that relies on a proximity criterion between submodels and the initial one. These approaches are compared with RSIR and SR-SIR in a simulation study. Finally we applied SIR-QZ and the associated selection procedure to a genetic dataset in order to find eQTL.

Domaines: Méthodologie [stat.ME]

Raphaël Coudret, Benoit Liquet, Jerôme Saracco. Comparison of sliced inverse regression approaches for underdetermined cases. Journal de la Société Française de Statistique, 2014, 155 (2). ⟨hal-00768352⟩