Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By using the fused lasso penalty over a $K$-nearest neighbors graph, we propose an adaptive quantile estimator in a non-parametric setup. We show that the estimator attains optimal rate of $n^{-1/d}$ up to a logarithmic factor, under mild assumptions on the data generation mechanism of the $d$-dimensional data. We develop algorithms to compute the estimator and discuss methodology for model selection. Numerical experiments on simulated and real data demonstrate clear advantages of the proposed estimator over state of the art methods.
翻译:量化回归是一种统计方法,用于估算响应变量的有条件量化。此外,对于平均估算,众所周知,量化回归比以美元=2美元为基础的方法对外值更为坚固。通过对最近的邻里图形使用结合的拉索罚款,我们提议在非参数设置中采用适应性量化估计器。我们显示,根据对美元=维数据数据的数据生成机制的微小假设,估算器达到最高至对数系数的美元=1/d}。我们开发算法,以计算估计器并讨论模型选择方法。模拟和真实数据的数值实验显示了拟议估算器相对于艺术方法状态的明显优势。