Box-Cox变换用于分位数回归曲线相交问题的研究  

Apply Box-Cox Transformation to the Research on Crossing Problems of Quantile Regression

作　　者：王欢[1] 袁永生[1] 

机构地区：[1]河海大学理学院,江苏南京210098

出　　处：《数理统计与管理》2009年第6期1024-1029,共6页Journal of Applied Statistics and Management

摘　　要：将Box-Cox变换与分位数回归模型相结合(两阶段法),是分位数回归研究领域的一大进步。该法虽然两步都与分位数回归的检验函数紧密结合,但是由于没有利用分位数回归的优良性质,而是引入了中间参变量,因此增加了模型的累进误差,降低了模型精度。更重要的是,两阶段法没有对于分位数回归领域中普遍出现的分位数回归曲线的相交问题给出解决方法。针对这些问题,经研究应该首先确定Box-Cox变换的参数,避免模型中不确定因素的引入,然后对数据进行整体变换并结合分位数检验函数,直接利用分位数回归的优良性质,最终确定分位数回归模型的参数。实例证明,该方法提高了模型的精度,可以有效地解决分位数回归曲线的相交问题。It is a great progress in quantile regression area that quantile regression method is combined with Box-Cox transformation（called‘tow- stage method ）.Though the two- stage method is closely tied to quantile regression,the two-stage method uses mid-variables,so the error of the model increases while the accuracy of the model declines.Even more,the two-stage method does not give out a good solution to the crossing problem which is common in quantile regression area.Aiming at handling those problems mentioned above, this paper first figures out the accurate parameter of Box-Cox transformation, avoiding the uncertain factors and then transforms the data as a whole, making good use of the properties of quantile regression and its check function, finally fixes the parameters in the quantile regression model. The example in this paper gives a good proof that the method here can solve the crossing problem of quantile regression while increasing accuracy.

关 键 词：分位数回归 数据变换 Box-Cox变换 检验函数 

分 类 号：O212.1[理学—概率论与数理统计] TP242.6[理学—数学]