变系数混合效应模型

本文研究了下列变系数混合效应模型: $y_{ij}=z_{ij}^{\tau}b_i+x_{ij}^{\tau}\beta(w_{ij}) +\xe_{ij},i=1,\cdots,m;j=1,\cdots,n_i$, 其中$b_i$为i.i.d.期望为$\xt$, 协方差阵为$\xs^2_bI_q$的随机效应向量, $\xe_{ij}$是i.i.d.期望为零, 具有有限方差的随机误差. 文中我们不仅给出了函数系数向量$\xb(\cdot)$的局部多项式估计, 同时给出了随机效应期望、方差和随机误差方差的估计, 并给出了这些估计量的渐进正态性和相合性, 研究结果表明了这些估计量的可靠性.

On Varying Coefficient Mixed-Effects Model

In this paper we consider the following varying coefficient mixed-effects model:$y_{ij}=z_{ij}^{\tau}b_{i}+x_{ij}^{\tau}\beta(w_{ij})+\xe_ij},i=1,\cdots,m;j=1,\cdots,n_i$, where $b_{i}$ is i.i.d. random effects with mean vector $\theta$ and covariance matrix $\sigma_{b}^{2}I_{q}$, $\xe_{ij}$ 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.