In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is non-smooth as in the case of quantile regression. In this paper, we develop methods for the modeling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. This work represents an extension of the linear quantile mixed models of Geraci and Bottai (2014, Statistics and Computing). We develop a novel algorithm which is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. To assess the proposed methods, we present a simulation study and two applications, one in pharmacokinetics and one related to growth curve modeling in agriculture.

中文翻译：

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聚类数据非线性分位数回归的建模和估计

在回归应用中，观测值之间非线性和相关性的存在不仅在最小二乘回归等传统设置中带来了计算挑战，而且（尤其是）当目标函数不平滑（如分位数回归）时也带来了计算挑战。在本文中，我们开发了当数据在两级嵌套设计中聚类时非线性条件分位数函数的建模和估计方法。这项工作代表了 Geraci 和 Bottai（2014 年，统计与计算）线性分位数混合模型的扩展。我们开发了一种新颖的算法，它混合了分位数回归的平滑算法和非线性混合模型的二阶拉普拉斯近似。为了评估所提出的方法，我们提出了一项模拟研究和两个应用，一个在药代动力学中，一个与农业中的生长曲线建模相关。