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Multivariate quantile regression tree
Journal of the Korean Data & Information Science Society 2017;28:533-45
Published online May 31, 2017
© 2017 Korean Data & Information Science Society.

Jaeoh Kim1 · HyungJun Cho2 · Sungwan Bang3

12Department of Statistics, Korea University
3Department of Mathematics, Korea Military Academy
Correspondence to: Sungwan Bang
Associate professor, Department of Mathematics, Korea Military Academy, 574, Hwarang-ro, Nowon-gu, Seoul, Korea. E-mail:
Received April 18, 2017; Revised May 24, 2017; Accepted May 27, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Quantile regression models provide a variety of useful statistical information by estimating the conditional quantile function of the response variable. However, the traditional linear quantile regression model can lead to the distorted and incorrect results when analysing real data having a nonlinear relationship between the explanatory variables and the response variables. Furthermore, as the complexity of the data increases, it is required to analyse multiple response variables simultaneously with more sophisticated interpretations. For such reasons, we propose a multivariate quantile regression tree model. In this paper, a new split variable selection algorithm is suggested for a multivariate regression tree model. This algorithm can select the split variable more accurately than the previous method without significant selection bias. We investigate the performance of our proposed method with both simulation and real data studies.
Keywords : Data mining, multivariate data analysis, quantile regression, regression tree.