Application of the bootstrap approach to the choice of dimension and the α parameter in the SIRα method

Jerome Saracco (1) , Benoit Liquet (2)

1 GREThA - Groupe de Recherche en Economie Théorique et Appliquée
2 Biostatistique

Sliced inverse regression allows to determine linear combinations of a covariable X related to a response Y in semiparametric regression. The determination of a suitable dimension is important. Statistical tests based on nullity of some eigenvalues have been proposed. Another approach is to consider the quality of the estimation of the effective dimension reduction (EDR) space. The square trace correlation between the EDR space and its estimate can be used . We focus on SIRα and propose a bootstrap estimation of this criterion which could also select the α parameter. A simulation study is performed to illustrate the numerical behaviour.

Mots clés: Physical Sciences

Jerome Saracco, Benoit Liquet. Application of the bootstrap approach to the choice of dimension and the α parameter in the SIRα method. Communications in Statistics - Simulation and Computation, 2008, 37 (06), pp.1198-1218. ⟨10.1080/03610910801889011⟩. ⟨hal-00514324⟩