Testing in generalized partially linear models: A robust approach

Abstract

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) + x t i β  and H a known link function, we want to test H0 : η(t) = α + γ t against H1 : 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