Semiparametric Hierarchical Composite Quantile Regression

• Published in: Communications in statistics. Theory and methods Vol. 44; no. 5; pp. 996 - 1012
• Main Authors: Chen, Yanliang, Tang, Man-Lai, Tian, Maozai
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.03.2015; Taylor & Francis Ltd
• Subjects: Composite quantile regression; Economic models; Flexibility; Hierarchical data; Hierarchies; Least squares method; Mathematical analysis; MM algorithm; Multilevel; Primary 62G05; Quantiles; Regression; Regression analysis; Secondary 62G20; Semiparametric model; Statistics
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2012.755199

In biological, medical, and social sciences, multilevel structures are very common. Hierarchical models that take the dependencies among subjects within the same level are necessary. In this article, we introduce a semiparametric hierarchical composite quantile regression model for hierarchical data. This model (i) keeps the easy interpretability of the simple parametric model; (ii) retains some of the flexibility of the complex non parametric model; (iii) relaxes the assumptions that the noise variances and higher-order moments exist and are finite; and (iv) takes the dependencies among subjects within the same hierarchy into consideration. We establish the asymptotic properties of the proposed estimators. Our simulation results show that the proposed method is more efficient than the least-squares-based method for many non normally distributed errors. We illustrate our methodology with a real biometric data set.