一种完全数据驱动的众数回归模型估计方法

Totally Data-driven Estimations of Modal Regression Models

众数回归是比均值回归更稳健的回归模型,该模型的PMS估计方法基于核密度估计及梯度上升算法,求解过程存在边界效应差、非全局最优、效率低等缺陷。给出一种完全数据驱动的众数回归模型估计方法。通过搜索最优覆盖区间,进而估计条件众数。该方法不借助核密度估计,超参数选择、迭代过程完全由数据驱动,无需交叉验证的计算负担。模拟和实际应用结果显示该方法计算效率高,拟合效果良好,比PMS算法易于应用。

Modal regression models have more robustness than mean regression models,their common PMS solutions are based on kernel density estimations and gradient ascending algorithm and with the shortcomings of poor boundary effect,non-global optimum and low computational efficiency.The totally data-driven estimations of modal regression models are proposed.The conditional modes are estimated by searching the optimal covering intervals,but not depend on the kernel density estimations,the hyper-parameters selections and iterations are all data-driven and without the cost of cross-validation.The simulations and application show that this method performs as well as PMS on estimations and is more convenient to use.