On Varying Coefficient Mixed-Effects Model

In this paper we consider the following varying coefficient mixed-effects model: y_ij=z_ij^\taub_i+x_ij^\tau\beta(w_ij) +\xe_ij,\;i=1,\cdots,m;\;j=1,\cdots,n_i, where b_i is i.i.d. random effects with mean vector \theta and covariance matrix \sigma_b^2I_q, \xe_ij is i.i.d. random errors with zero mean and finite variance. The local polynomial estimator of the function coefficient vector \beta(\cdot) is proposed. The method for estimating the mean of random effects, variances of random effects and random errors are also given. Asymptotic normality and consistency for the estimators are established, which give useful insight into the reliability of these general estimation methods.