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 y(i)vertical bar (x(i), t(1)) similar to F (center dot, mu(i)) with mu(i) = H (eta(t(i)) + x(i)(T) beta) and H a known link function, we want to test H-0 : eta(t) = alpha + gamma t against H-1 : eta 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. (C) 2012 Elsevier B.V. All rights reserved.