论文标题
通过K-NN融合拉索的非参数分位数回归
Non-parametric Quantile Regression via the K-NN Fused Lasso
论文作者
论文摘要
分位数回归是一种统计方法，用于估计响应变量的条件分位数。此外，对于平均估计，众所周知，与基于$ l_2 $的方法相比，分位数回归对离群值更强。通过在$ k $ neart的邻居图上使用融合的套索惩罚，我们建议在非参数设置中进行自适应分位数估计器。我们表明，在对$ d $维数据的数据生成机制的轻度假设下，估算器的最佳率达到了对数因子的最佳速率。我们开发算法来计算估计器并讨论模型选择的方法。对模拟和真实数据的数值实验证明了拟议估计量比最先进的方法的明确优势。
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.
