Testing in generalized partly linear models: A robust approach

BOENTE, GRACIELA; CAO, RICARDO; GONZALEZ-MANTEIGA, WENCESLAO; RODRIGUEZ, DANIELA

STATISTICS & PROBABILITY LETTERS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2013 vol. 83 p. 203 - 212

0167-7152

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 $y_i| (x_i,t_})~F(., mu_i)$ 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.