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Semiparametric inference in generalized mixed effects models. (English) Zbl 1411.62085

Summary: The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines likelihood approaches for mixed effects models, with kernel methods. Following the methodology of W. Härdle et al. [Econom. Theory 20, No. 2, 265–300 (2004; Zbl 1072.62034)], we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated by using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behaviour of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.

MSC:

62G05 Nonparametric estimation
62J12 Generalized linear models (logistic models)
86A32 Geostatistics

Citations:

Zbl 1072.62034
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