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Abstract
For exhibiting dependence among the observations within the same subject, the paper considers the estimation problems of partially linear models for longitudinal data with the φ-mixing and ρ-mixing error structures, respectively. The strong consistency for least squares estimator of parametric component is studied. In addition, the strong consistency and uniform consistency for the estimator of nonparametric function are investigated under some mild conditions.
Highlights
Longitudinal data (Diggle et al [1]) are characterized by repeated observations over time on the same set of individuals
We assume that the full dataset {(xij, yij, tij), i = 1,..., n, j = 1,..., mi}, where n is the number of subjects and mi is the number of repeated measurements of the ith subject, is observed and can be modeled as the following partially linear models yij = xTij β + g(tij) + eij, (1:1)
For assessing estimator of the nonparametric component g(·), we study the square root of mean-squared errors (RMSE) based on 1000 repetitions
Summary
Longitudinal data (Diggle et al [1]) are characterized by repeated observations over time on the same set of individuals. Some authors have not considered the with-subject dependence to study the asymptotic behaviors of estimation in the semipara-metric models with assumption that the mi are all bounded, see, for example, He et al [21], Xue and Zhu [22] and the references therein. We consider the estimation problems for the models (1.1) with the -mixing and r-mixing error structures for exhibiting dependence among the observations within the same subject respectively and are mainly devoted to strong consistency of estimators.
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