On applications of semiparametric Multiple Index regression

Generalized linear models (GLM) have been used as a classical parametric method for estimating a conditional regression function. We intend to examine the practical performance of Multiple-Index Modelling (MIM) as an alternative semiparametric approach. We focus specially on models with binary response Y and multivariate covariates X. We shall use two methods to estimate a regression function among which the refined Outer Product Gradient (rOPG) and the refined Minimum Average Variance Estimation (rMAVE) defined in Xia et al. (2002). We will show here by simulation argument that Multiple-Index modelling appears to be much more efficient than the GLM methodology and its usual Single-Index modelling (SIM) generalization to modelize the regression function.