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Abstract:
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Methods of estimating parametric and nonparametric components have been examined in partially linear models. These models are appealing due to their flexibility and wide range of practical applications. The compound estimator (Charnigo, Feng and Srinivasan, 2015) has been used to estimate the nonparametric component of such a model, in conjunction with linear mixed modeling for the parametric component. These authors showed, under a strict orthogonality condition, that the parametric and nonparametric component estimators were (nearly) optimal, even in the presence of subject-specific random effects. Without orthogonality, iterative backfitting could be used to achieve convergence of both parametric and nonparametric estimators. However, the theoretical properties of those backfitted estimators are not established. Therefore, we now study both parametric and nonparametric estimators in a partially linear model with random effects, to extend the consistency results of Charnigo et al (2015) to a non-orthogonal design and those of Levine (2015) to correlated data. The random effects accommodate analysis of individuals on whom repeated measures are taken.
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