基于B样条的众数回归模型

袁万里,杨联强,王学军

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (11) : 2125-2135.

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系统科学与数学 ›› 2020, Vol. 40 ›› Issue (11) : 2125-2135. DOI: 10.12341/jssms14023
论文

基于B样条的众数回归模型

    袁万里,杨联强,王学军
作者信息 +

Modal Regression Models Based on B-Splines

    YUAN Wanli ,YANG Lianqiang ,WANG Xuejun
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摘要

文章给出一种基于B样条的非参数众数回归模型以及一种适合于众数回归模型的交叉验证超参数选择准则. 现有的非参数局部多项式众数回归模型估计效果良好, 但该方法计算复杂度较高. 为了弥补该缺陷, 利用B样条的优良性质, 给出了一种基于B样条的非参数众数回归方法. 和局部多项式模型相比, 该方法估计效果相近, 但计算复杂度大为降低. 另外, 针对常用的交叉验证超参数选择准则不适用于众数回归这一现象, 给出了一种新的交叉验证超参数选择准则, 模拟和实例结果表明, 该方法在超参数选择中表现优良.

Abstract

A nonparametric model based on B-Splines and a cross-validation criterion for hyperparameter selection are given for modal regression. The existing nonparametric local polynomial modal regression performs well in the goodness of fit, but with a high computational complexity. Owing to the nice properties of B-Splines, modal regression based on B-Splines performs comparably with the local polynomial modal regression on estimation but spends much less computational burden. Furthermore, because the commonly used cross-validation hyperparameter selection criteria are not suitable to modal regression, we construct a new cross-validation hyperparameter selection criterion. Simulations and application show that this criterion behaves well for modal regression.

关键词

众数回归 / B样条 / EM算法 / 超参数选择.

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袁万里 , 杨联强 , 王学军. 基于B样条的众数回归模型. 系统科学与数学, 2020, 40(11): 2125-2135. https://doi.org/10.12341/jssms14023
YUAN Wanli , YANG Lianqiang , WANG Xuejun. Modal Regression Models Based on B-Splines. Journal of Systems Science and Mathematical Sciences, 2020, 40(11): 2125-2135 https://doi.org/10.12341/jssms14023
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