Semiparametric Hierarchical Composite Quantile Regression |
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Authors: | Yanliang Chen Man-Lai Tang Maozai Tian |
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Affiliation: | 1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou, China;2. School of Statistics, Renmin University of China, Beijing, Chinamltang@hsmc.edu.hk;4. Department of Mathematics and Statistics, Hang Seng Management College, Shatin, Hong Kong, China;5. School of Statistics, Renmin University of China, Beijing, China |
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Abstract: | 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. |
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Keywords: | Composite quantile regression Hierarchical data MM algorithm Semiparametric model |
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