摘要
分位数回归方法由于其具有稳健性,不仅能够全面刻画响应变量的条件分布,还能提供更有现实意义的回归参数,已经逐渐成为各个领域统计分析的强有力的工具.但在许多实际应用中,人们不仅想要探寻不同水平下(即不同分位数)响应变量与解释变量之间的关系,更希望找到一个最优水平,也即最优分位数,使其上的回归结果最真实可靠,最好地反映总体情况.文中提出一种新的回归方法一最优分位回归方法,给出此类问题一个完美的解决方案.该方法的灵感主要来源于稀疏函数的定义,可以证实与传统均值回归相比最优分位回归方法更具优势:(1)稳健性.不受误差分布的限制;(2)有效性.回归结果蕴含信息更丰富;(3)灵活性.对任意模型及数据均适用.文中的模拟结果也对以上三条性质给予极大的支持.最后食品消费数据的分析结果表明当考虑食品消费与人均收入的关系时,中下等收入人群的消费模式为社会的主流模式.
Quantile regression is becoming a powerful statistical tool in diverse fields, owing to its robustness, completeness and interpretability. However, in many real applications, not only the relationship between the response and covariates is to be investigated, but the best quantile level is more required. To this end, Optimal Quantile Regression (OQR) technique based on sparsity function is proposed. It can be demonstrated that the proposed OQR has significant advantages compared with classical mean regression.(1) Robustness,(2) Efficiency,(3) Flexibility. To examine the performance of proposed methods, simulations are conducted. The results all provide valid supports with the proposed OQR. In the end, a real data is used to make an illustration. It is suggested, in terms of salary, the lower class of people should be of more attention.
作者
熊巍
田茂再
XIONG Wei;TIAN Mao-zai(School of Statistics, Big Data and Risk Management Research Center, University of international Business and Economics, Beijing 100029, China;Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872,China;School of Statistics and Information, Xinjiang University of Finance and Economics, Urumqi 830012, China;School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730101, China)
出处
《高校应用数学学报（A辑）》
北大核心
2019年第1期25-43,共19页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
教育部人文社会科学研究青年基金(16YJCZH122)
对外经济贸易大学中央高校基本科研业务费专项资金(15QD15)
国家自然科学基金(11861042)
中国人民大学科学研究基金(中央高校基本科研业务费专项资金)(18XNL012)
全国统计科研计划项目重大项目(2016LD03)
中央高校建设世界一流大学(学科)和特色发展引导专项资金
关键词
稀疏函数
最优分位
分位数回归
稳健性
sparsity
optimal quantile
quantile regression
robustness
