分段线性删失分位数回归模型的变点估计  

Change point estimation of piecewise linear censored quantile regression model

作　　者：王小刚 冯可馨 WANG Xiaogang;FENG Kexin(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,Ningxia,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《山东大学学报（理学版）》2023年第11期35-44,共10页Journal of Shandong University(Natural Science)

基　　金：宁夏自然科学基金资助项目(2023AAC02043);宁夏高等教育一流学科建设基金资助项目(NXYLXK2017B09);北方民族大学服务宁夏九大产业基金资助项目(FWNX36);北方民族大学研究生创新项目(YCX21159)。

摘　　要：在删失分位数回归模型中引入分段线性结构,改进原有模型仅考虑线性结构、静态性和无交互效应等缺陷。分段线性的前提假设使得部分协变量在不同状态下呈现不同结构且在变点处连续,保留模型易于计算和解释性强的优点。基于格点搜索法得到变点位置和模型参数估计,推导估计的大样本性质。数值模拟结果验证不同误差结构下变点和模型参数估计具有有效性和稳健性。实证分析表明家庭金融资产与受教育水平正相关,且资产规模存在集聚效应,资产规模越大的家庭其金融资产越多。受教育水平在本科之前存在一个变点,突破受教育水平变点后,不同规模家庭的金融资产都有质的提升,但变点后高资产规模家庭的金融资产增速要高于中低资产规模家庭的增速。A piecewise linear censored quantile regression model is proposed in censored data model,which could improve the shortcomings of linear structure,static and non-interaction effects.It assumes a piecewise linear form in different regions of the domain of partial covariate but still continuous at an unknown change point,which retaining the advantages of calculation and interpretability.The estimators for change point and regression coefficients are obtained via grid search method,the asymptotic normality of all parameters are derived.The effectiveness and robustness of the estimation are verified by numerical simulation in both homoscedastic and heteroscedastic cases.There is a positive correlation between household financial assets and educational level,the aggregation effect is found in the scale of assets,that is,the financial assets are more when the scale of the households were larger.There is a change point in the educational level before undergraduate,and the financial assets improve qualitatively after breaking through the change point of educational level.The growth rate of financial assets of high-asset households are higher than that of low and medium-asset households.

关 键 词：变点估计 删失分位数回归模型 格点搜索法 大样本性质 分段线性结构 

分 类 号：O212.2[理学—概率论与数理统计]