We propose a nonparametric method for estimating the conditional quantile function that admits a generalized additive specification with an unknown link function. This model nests single-index, additive, and multiplicative quantile regression models. Based on a full local linear polynomial expansion, we first obtain the asymptotic representation for the proposed quantile estimator for each additive component. Then, the link function is estimated by noting that it corresponds to the conditional quantile function of a response variable given the sum of all additive components. The observations are supposed to be a sample from a strictly stationary and absolutely regular process. We provide results on (uniform) consistency rates, second order asymptotic expansions and point wise asymptotic normality of each proposed estimator.

翻译：我们提出了一种非参数方法，用于估计带有未知链接函数的广义可加设定下的条件分位数函数。该模型包含了单指标、可加和乘性分位数回归模型。基于完整的局部线性多项式展开，我们首先获得了每个可加分量所提分位数估计量的渐近表示。随后，通过注意到链接函数对应于在给定所有可加分量的和的情况下响应变量的条件分位数函数，对该函数进行了估计。观测值假定来自严格平稳且完全正则的过程。我们给出了每个估计量的（一致）收敛速度、二阶渐近展开以及逐点渐近正态性的结果。