The frequentist model averaging (FMA) and the focus information criterion (FIC) under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claeskens in 2003. One inconvenience, however, of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression (QR). This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model. Specifically, we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter. Then based on this asymptotic result, we develop the FIC and FMA in the current setting. Our theoretical development depends crucially on the convexity of the objective function, which makes possible to establish the asymptotics based on the existing convex stochastic process theory. Simulation studies are presented to illustrate the finite sample performance of the proposed method. The low birth weight data set is analyzed.

自2003年Hjort和Claeskens的开创性工作以来，在可能性和回归设置下，对本地框架下的常客模型平均（FMA）和焦点信息标准（FIC）进行了广泛的研究。但是，现有工作的不便之处在于他们通常要求所涉及的标准函数必须是两次可微的，因此阻止了直接应用于分位数回归（QR）的情况。QR的这种以及其他固有优点促使我们去研究本地错误指定的线性QR模型中的FIC和FMA。具体来说，我们在本文中得出了基于一般基于子模型的焦点参数QR估计量的显式渐近风险表达。然后根据此渐近结果，在当前设置下开发FIC和FMA。我们的理论发展主要取决于目标函数的凸性，这使得有可能基于现有的凸随机过程理论建立渐近性。仿真研究表明了该方法的有限样本性能。分析低出生体重数据集。