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Multi-step quantile regression tree. (English) Zbl 1453.62452
Summary: Quantile regression (QR) proposed by R. Koenker and G. Bassett jun. [Econometrica 46, 33–50 (1978; Zbl 0373.62038)] is a statistical technique that estimates conditional quantiles. It has been widely studied and applied to economics. N. Meinshausen [J. Mach. Learn. Res. 7, 983–999 (2006; Zbl 1222.68262)] proposed quantile regression forests (QRF), a non-parametric way based on random forest. QRF performs well in terms of prediction accuracy, but it struggles with noisy data sets. This motivates us to propose a multi-step QR tree method using GUIDE (Generalized, Unbiased, Interaction Detection and Estimation) made by W.-Y. Loh [Stat. Sin. 12, No. 2, 361–386 (2002; Zbl 0998.62042)]. Our simulation study shows that the multi-step QR tree performs better than a single tree or QRF especially when it deals with data sets having many irrelevant variables.
MSC:
62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
68T05 Learning and adaptive systems in artificial intelligence
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