In this article, we propose a high dimensional semiparametric model average approach to predict the conditional quantile of the response variable. Firstly, we approximate the multivariate conditional quantile function by an affine combination of one-dimensional marginal conditional quantile functions which can be estimated by the local linear regression. Secondly, based on the estimated marginal quantile regression functions, a penalized quantile regression is proposed to estimate and select the significant model weights involved in the approximation. Under some mild conditions, we have established the asymptotic properties for both the parametric and nonparametric estimators. Finally, we evaluate the finite sample performance of the proposed procedure via simulations and a real data analysis.

中文翻译：

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高维条件分位数预测的模型平均边际回归

在本文中，我们提出了一种高维半参数模型平均方法来预测响应变量的条件分位数。首先，我们通过可以通过局部线性回归估计的一维边缘条件分位数函数的仿射组合来近似多元条件分位数函数。其次，基于估计的边际分位数回归函数，提出了惩罚分位数回归来估计和选择近似中涉及的显着模型权重。在一些温和的条件下，我们已经建立了参数和非参数估计量的渐近性质。最后，我们通过模拟和真实数据分析来评估所提出程序的有限样本性能。