基于非参数分位数估计的众数回归模型

Modal Regression Based on Nonparametric Quantile Estimator

本文给出基于非参数分位数估计的众数回归模型.不同于传统的均值和中位数回归模型,众数回归模型使用条件众数刻画分布的中心,在数据分布存在异常值、非对称或重尾这些特征时,具有更好的稳健性.当前众数回归模型的解法主要是基于条件密度的核估计方法.本文给出一种新的基于非参数分位数估计的众数回归模型求解方法.该方法通过分布函数与分位数函数的互逆性来估计众数,从而可以充分利用非参数分位数估计的灵活性.模拟和实际应用结果显示,该方法表现良好,优于基于线性分位数估计的众数回归模型.

Modal regression based on nonparametric quantile estimator is given.Unlike the traditional mean and median regression,modal regression uses mode but not mean or median to represent the center of a conditional distribution,which helps the model to be more robust for outliers,asymmetric or heavy-tailed distribution.Most of solutions for modal regression are based on kernel estimation of density.This paper studies a new solution for modal regression by means of nonparametric quantile estimator.This method builds on the fact that the distribution function is the inverse of the quantile function,then the flexibility of nonparametric quantile estimator is utilized to improve the estimation of modal function.The simulations and application show that the new model outperforms the modal regression model via linear quantile function estimation.