含多变点的删失分位数回归模型统计推断及应用  

Statistical Inference for the Censored Quantile Regression Model with Multiple Change Points

作　　者：王小刚 陈姜猛 张飞鹏 WANG Xiaogang;CHEN Jiangmeng;ZHANG Feipeng(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021;School of Economics and Finance,Xi'an Jiaotong University,Xi'an 710049)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021 [2]西安交通大学经济与金融学院,西安710049

出　　处：《系统科学与数学》2023年第6期1612-1634,共23页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(72171192);宁夏自然科学基金(2021AAC03186);宁夏高等教育一流学科建设基金(NXYLXK2017B09);北方民族大学服务宁夏九大产业项目(FWNX36)资助课题。

摘　　要：文章考虑含多个变点的删失分位数回归模型,借助线性化技术与迭代更新算法提出可以同时估计变点个数、变点位置及模型回归参数的估计方法,推导了变点个数选择的相合性,证明变点位置与回归参数具有相合性与渐近正态性.为了检验变点存在性,提出了一个基于残差加权的CUSUM检验统计量,并推导了其极限性质.数值模拟结果表明所提估计与检验方法在同方差、异方差情形下都具有良好的有限样本表现.最后,运用该模型对中国家庭金融资产进行实证分析,验证了所提方法的可行性与有效性.This paper considers a censored quantile regression model with multiple change points.By the linearizatin technique,we propose an iterative segmented algorithm via bootstrap and backward elimination algorithm by BIC criterion to simultaneously estimate the number and locations of change points and regression coefficients.We establish their asymptotic properties,including the selection consistency of the number of change points,the consistency and asymptotic normality of the estimators of location of change points and regression coefficients.A weighted CUSUM test statistic is developed for the existence of a change point at a quantile level,and its limiting distribution is also established.Numerical studies show that the proposed estimating and test methods have good finite sample performance in both homoscedastic and heteroscedastic cases.An application to the Chinese household financial assets data illustrates the usefulness and validity of the proposed method.

关 键 词：多变点 删失分位数回归模型 BIC准则 线性化技术 反向消除 

分 类 号：O212.1[理学—概率论与数理统计]