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Hierarchical linear regression models for conditional quantiles

Science China Mathematics 2006年第12期49卷 1800-1815页

作者： TIAN Maozai & CHEN Gemai School of Statistics, Renmin University of China, Beijing 100872, China and Center for Applied Statistics, Renmin University of China, Beijing 100872, China Department of Mathematics and Statistics, University of Calgary, Canada School of Statistics Renmin University of China Beijing 100872 China Department of Mathematics Statistics University of Calgary Canada Center for Applied Statistics Renmin University of China Beijing 100872 China

The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models,but it cannot deal effectively with the data with a hierarchical *** practice,the existence of such data hierarchies is neither accidental nor ignorable,it is a common *** ignore this hierarchical data structure risks overlooking the importance of group effects,and may also render many of the traditional statistical analysis techniques used for studying data relationships *** the other hand,the hierarchical models take a hierarchical data structure into account and have also many applications in statistics,ranging from overdispersion to constructing min-max ***,the hierarchical models are virtually the mean regression,therefore,they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional ***,the estimated coefficient vector (marginal effects)is sensitive to an outlier observation on the dependent *** this article,a new approach,which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models,is *** the theoretical front,we also consider the asymptotic properties of the new method,obtaining the simple conditions for an n1/2-convergence and an asymptotic *** also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.

关键词： hierarchical quantile regression models,EQ algorithm,fixed effects,random effects,regression quantile.

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