ABSTRACT

In this paper, we develop a model averaging estimation procedure for multiple quantile regression where missingness occurs to the covariates. Our concern is on the improvement of prediction accuracy for multiple quantiles of response conditional on observed covariates. A set of candidate models is constructed according to missingness data patterns. In this model set, one model is based on the subjects with complete-case data, and the remaining models are based on the subsets of covariates with observed data. The weights for our model averaging are determined by a leave-one-out cross-validation criterion that is minimized over the complete case datasets. Under certain regularity conditions, we establish the asymptotic optimality for the selected weights in the sense of minimizing the out-of-sample combined quantile prediction error. Simulation studies are presented to demonstrate the advantages of the proposed approach vs. several existing active methods. As an illustration, a dataset from NHANES 2005-2006 is analysed.

摘要

在本文中，我们为多分位数回归开发了一个模型平均估计程序，其中协变量发生缺失。我们关注的是提高以观察到的协变量为条件的响应的多个分位数的预测准确性。根据缺失数据模式构建一组候选模型。在该模型集中，一个模型基于具有完整案例数据的受试者，其余模型基于具有观察数据的协变量子集。我们模型平均的权重由留一法交叉验证标准确定，该标准在整个案例数据集上最小化。在一定的规律性条件下，我们在最小化样本外组合分位数预测误差的意义上为所选权重建立渐近最优性。提供模拟研究以证明所提出的方法与几种现有的主动方法相比的优势。作为说明，分析了来自 NHANES 2005-2006 的数据集。