Composite hierachical linear quantile regression

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• 作者：Yan-liang Chen (1)
  Mao-zai Tian (1)
  Ke-ming Yu (2) (3)
  Jian-xin Pan (4) (5)
  
  1. Center for Applied Statistics ; School of Statistics ; Renmin University of China ; Beijing ; 100872 ; China
  2. School of Business ; Shihezi University ; Shihezi ; 832003 ; China
  3. Mathematical Sciences ; John Crank 209 ; Brunel University ; Uxbridge ; UB8 3PH ; UK
  4. School of Mathematics ; The University of Manchester ; Oxford Road ; Manchester ; M13 9PL ; UK
  5. School of Statistics and Mathematics ; Yunnan University of Finance and Economics ; Kunming ; 650221 ; China
  
• 关键词：multilevel model ; composite quantile regression ; E ; CQ algorithm ; fixed effects ; random effects ; 62G05 ; 62G20 ; 60G42
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：30
• 期：1
• 页码：49-64
• 全文大小：311 KB
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• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

Multilevel (hierarchical) modeling is a generalization of linear and generalized linear modeling in which regression coefficients are modeled through a model, whose parameters are also estimated from data. Multilevel model fails to fit well typically by the use of the EM algorithm once one of level error variance (like Cauchy distribution) tends to infinity. This paper proposes a composite multilevel to combine the nested structure of multilevel data and the robustness of the composite quantile regression, which greatly improves the efficiency and precision of the estimation. The new approach, which is based on the Gauss-Seidel iteration and takes a full advantage of the composite quantile regression and multilevel models, still works well when the error variance tends to infinity. We show that even the error distribution is normal, the MSE of the estimation of composite multilevel quantile regression models nearly equals to mean regression. When the error distribution is not normal, our method still enjoys great advantages in terms of estimation efficiency.