基于核密度的变系数乘积模型估计  

Kernel Density Estimation for Varying Coefficient Multiplicative Model

作　　者：毛亚茜 赵培信[1,2] MAO Yaxi;ZHAO Peixin(School of Mathematics and Statistics,Chongqing Technology and Business University;Chongqing Key Laboratory of Statistical Intelligent Computing and Monitoring,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆南岸400067 [2]统计智能计算与监测重庆市重点实验室,重庆南岸400067

出　　处：《四川文理学院学报》2025年第2期128-132,共5页Sichuan University of Arts and Science Journal

基　　金：国家社会科学基金一般项目(18BTJ035);重庆市自然科学基金面上项目(cstc2020jcyj-msxmX0006)。

摘　　要：针对变系数乘积模型的估计问题,提出了一种基于核密度的估计方法;该估计方法中,允许未知密度函数的模型误差为多峰或具有较大方差;同时,为了解决部分数据个体之间的测量单位不同,结合B样条函数方法和最小乘积相对误差(LPRE)准则,求解目标函数一阶偏导数的根,进而得到了最小乘积相对误差估计量;最后,在一定正则条件下,理论证明了所提出的估计的渐近正态性和相合性,进一步表明提出的估计量具有稳健性.Focusing on the estimation problem of varying coefficient multiplicative models,this study proposes a kernel density-based estimation method.This method allows the model error with an unknown density function to be multimodal or exhibit a large variance.To address the issue of differing measurement units among individual data points the Bspline function method is combined with the minimum product relative error LPRE criterion.By solving the roots of the first-order partial derivatives of the objective function,the minimum product relative error estimator is derived.Finally,under certain regular conditions,the asymptotic normality and coincidence of the proposed estimator are theoretically established,further demonstrating its robustness.

关 键 词：变系数模型 核密度估计 最小乘积相对误差 

分 类 号：O141.2[理学—数学]