Testing in generalized partially linear models: A robust approach

Graciela Boente, Ricardo Cao, Wenceslao González Manteiga and Daniela Rodriguez

Statistics & Probability Letters, 2013, vol. 83, issue 1, 203-212

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)+xit β) and H a known link function, we want to test H0:η(t)=α+γt 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.

Keywords: Generalized partially linear models; Kernel weights; Rate of convergence; Robust testing (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2012.08.031

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