非参数混合效应模型的估计

针对非参数混合效应模型提出估计方法,通过B样条的方法估计非参数函数,使用惩罚(非加权)最小二乘方法估计随机效应,然后通过构造正态似然函数得到方差的估计,并且证明了方差分量的相合性和函数部分的渐近正态性;最后给出数字模拟来展示所提出方法的估计效果,结果表明:该方法给出的估计效果良好,且在数值上是稳定的。

The Estimation for the Nonparametric Mixed Effects Model

The estimation methodology for the nonparametric mixed effects model is proposed. For this, we use the B splines methods to estimate the function, and employ the penalized least square method to obtain the estimator of the random effects. Further, we construct the normal likelihood function to estimate the variance components. And we also prove the consistency of variance components and the asymptotic normality of the link function.A simulation study is carried out to show the estimation effect of our proposed methodology.It shows our proposed methodology performs well.Our algorithm is stable numerically.