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) + 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 obtainedThis research was partially supported by Grants 20020100100276 and 20020100300057 from the Universidad de Buenos Aires, pip 112-200801-00216 from conicet, pict 0821 from anpcyt at Argentina and also by Spanish Grant MTM2008- 03010/MTM of the Ministerio Español de Ciencia e Innovación and XUNTA Grant 10MDS207015PRS