Inference for Optimal Split Point in Conditional Quantiles

• Published in: Frontiers of economics in China Vol. 11; no. 1; pp. 40 - 59
• Main Authors: Fan, Yanqin, Liu, Ruixuan, Zhu, Dongming
• Format: Journal Article
• Language: English
• Published: Beijing Higher Education Press 01.03.2016; Higher Education Press Limited Company
• Subjects: Analysis; Approximation; Asymptotic methods; Chernof distribution; cubic-root asymptotics; Decision tree; Decision trees; Econometric models; Mathematical functions; misspecified Quantile regression; optimal split point; Quantile regression; Statistical inference; Studies; 二元决策树; 分割点; 参数估计; 推理过程; 条件分位数; 极限分布; 测量实验; 逼近函数; China
• ISSN: 1673-3444; 1673-3568
• DOI: 10.3868/s060-005-016-0004-6

In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree is conducted by inverting a t-test or a deviation measure test, both involving Chemoff type limiting distributions. In order to avoid estimating the nuisance parameters in the complicated limiting distribution, subsampling is proved to deliver the correct confidence interval/set.