基于半参数混合效应模型的最优模型平均预测

Optimal Model Averaging Prediction in Semi-Parametric Mixed EffectModels

在对纵向数据的预测过程中,通常会遭遇模型的不确定问题.为了解决模型不确定性问题,文章提出一种基于半参数混合效应模型的最优模型平均预测方法.文章提出采用删组交叉验证的方法获得最优权重向量的估计,进而获得最终的模型平均预测值.理论上,文章证明了当所有候选模型均误设定时,所提出的模型平均估计具有渐近最优性.即,提出的模型平均估计量的二次损失渐近地达到了用该集合中权重进行加权的所有模型平均估计的二次损失下确界.另一方面,当候选模型中包含正确模型时,证明了提出的权重估计方法,在大样本意义下能够将权重分配给正确模型.模拟和实际数据分析表明,所提出的模型平均估计方法与一些常用的方法相比具有较好的预测性能.

Model uncertainty usually exists in the prediction for longitudinal data.To solve model uncertainty,we propose an optimal model averaging prediction method based on semi-parametric mixed effect models.The optimal weight vector is obtained by minimizing a leave-subject-out cross-validation.This paper shows that when all candidate models are misspecified,our proposed method is asymptotically optimal in the sense that it yields a squared prediction loss that is asymptotically identical to that resulting from the infeasible best-possible averaging estimator.In a different scenario,we show that our method can put the weight one to the correctly specified models.Both simulation study and empirical example show the superiority of our proposed estimator over other competitive methods.