Applying quantile regression to count data presents logical and practical complications which are usually solved by artificially smoothing the discrete response variable through jittering. In this paper, we present an alternative approach in which the quantile regression coefficients are modeled by means of (flexible) parametric functions. The proposed method avoids jittering and presents numerous advantages over standard quantile regression in terms of computation, smoothness, efficiency, and ease of interpretation. Estimation is carried out by minimizing a “simultaneous” version of the loss function of ordinary quantile regression. Simulation results show that the described estimators are similar to those obtained with jittering, but are often preferable in terms of bias and efficiency. To exemplify our approach and provide guidelines for model building, we analyze data from the US National Medical Expenditure Survey. All the necessary software is implemented in the existing R package qrcm.

应用分位数回归对数据进行计数会带来逻辑上和实际上的复杂性，通常可以通过抖动通过人为地平滑离散响应变量来解决这些复杂性。在本文中，我们提出了一种替代方法，其中分位数回归系数通过（灵活）参数函数建模。所提出的方法避免了抖动，并且在计算，平滑度，效率和易于解释方面均优于标准分位数回归。通过最小化普通分位数回归的损失函数的“同时”版本来进行估算。仿真结果表明，所描述的估计器与通过抖动获得的估计器相似，但在偏差和效率方面通常更可取。为了举例说明我们的方法并为建立模型提供指导，我们分析了来自美国国家医疗支出调查的数据。所有必需的软件都在现有的R包中实现qrcm。