To estimate the joint multivariate regression function, a robust ultra-high dimensional semiparametric model averaging approach is developed. Specifically, a three-stage estimation procedure is proposed. In the first step, the joint multivariate function can be approximated by a weighted average of one-dimensional marginal regression functions which can be estimated robustly by the composite quantile marginal regression. In the second step, a nonparametric composite quantile correlation screening technique is proposed to robustly choose relative important regressors whose marginal regression functions have significant effects on estimating the joint regression function. In the third step, based on these significant regressors that survive the screening procedure, a penalized composite quantile model averaging marginal regression is considered to further achieve sparse model weights and estimate the joint regression function. The sure independence screening property of the proposed screening procedure and sparse property of the penalized estimator are established under some regularity conditions. Numerical studies including both extensive simulation studies and an empirical application are considered to verify the merits of our proposed approach.

为了估计联合多元回归函数，开发了一种鲁棒的超高维半参数模型平均方法。具体来说，提出了一种三阶段估计程序。在第一步中，联合多元函数可以通过一维边际回归函数的加权平均值来近似，该加权平均值可以通过复合分位数边际回归进行稳健的估计。在第二步中，提出了一种非参数复合分位数相关性筛选技术来稳健地选择相对重要的回归变量，这些回归变量的边际回归函数对估计联合回归函数有显着影响。第三步，基于这些在筛选过程中仍然有效的回归因子，平均边际回归的惩罚复合分位数模型被认为可以进一步实现稀疏模型权重并估计联合回归函数。在一定的规律性条件下，建立了所提出的筛选过程的确定性独立筛选性质和惩罚估计量的稀疏性质。包括广泛的模拟研究和经验应用在内的数值研究被认为可以验证我们提出的方法的优点。