Boente Boente, GracielaCao Abad, Ricardo JoséGonzález Manteiga, WenceslaoRodríguez, Daniela2019-04-042019-04-042013Boente, G., Cao, R., González Manteiga, W., & Rodriguez, D. (2013). Testing in generalized partially linear models: A robust approach. Statistics & Probability Letters, 83(1), 203-212. doi: 10.1016/j.spl.2012.08.0310167-7152http://hdl.handle.net/10347/18530In 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 obtainedeng© 2013 Elsevier B.V. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Generalized partially linear modelsKernel weightsRate of convergenceRobust testingjournal article10.1016/j.spl.2012.08.031open access