Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

In this paper we consider the estimating problem of a semiparametric regression modelling when the data are longitudinal. An iterative weighted partial spline least squares estimator (IWPSLSE) for the parametric component is proposed which is more efficient than the weighted partial spline least squares estimator (WPSLSE) with weights constructed by using the within-group partial spline least squares residuals in the sense of asymptotic variance. The asymptotic normality of this IWPSLSE is established. An adaptive procedure is presented which ensures that the iterative process stops after a finite number of iterations and produces an estimator asymptotically equivalent to the best estimator that can be obtained by using the iterative procedure. These results are generalizations of those in heteroscedastic linear model to the case of semiparametric regression.