Testing in generalized partially linear models: A robust approach

In this paper, we introduce a family of robust statistics which allow to decide between a parametric model and a semiparametric one. More precisely, under a generalized partially linear model, i.e., when the observations satisfy yi|(xi,ti)∼F(⋅,μi) with μi=H(η(ti)+xit β) and HH a known link function, we want to test H0:η(t)=α+γtH0:η(t)=α+γt against H1:ηH1:η is a nonlinear smooth function. A general approach which includes robust estimators based on a robustified deviance or a robustified quasi-likelihood is considered. The asymptotic behavior of the test statistic under the null hypothesis is obtained.