1 论文标题：条件分位数的最优分割点推断

2 作者信息：范延琴，华盛顿大学；刘睿轩，埃默里大学；朱东明，上海财经大学

3 出处和链接：Yanqin Fan,Ruixuan Liu,Dongming Zhu. Inference for Optimal Split Point in Conditional Quantiles[J]. Front. Econ. China, 2016, 11(1): 40-59.

4 摘要：

在该文中我们使用协变量的二项决策函数（即两步阶梯函数）去近似条件分位数函数，证明了在这个错误设定的条件分位数模型里，其估计量呈现出立方根渐进性质。二项决策函数的最优分割点的推断是通过反转一个t检验或一个偏差测量检验来进行，二者都涉及切尔诺夫极限分布。为避免估计复杂极限分布中的多余参数，子样本抽样被证明可以提供正确的置信区间/集。

Editor’s Note:We are pleased to presentan article “Inferencefor Optimal Split Point in Conditional Quantiles”, written by Yanqin Fan (Universityof Washington), Ruixuan Liu (Emory University) and Dongming Zhu (ShanghaiUniversity of Finance and Economics), published in the Special Issue in Honorof Gregory Chow (Part I) in the Frontiersof Economics in China (FEC). The FEC is a quarterlypeer-reviewed journal edited by Institute for Advanced Research, Shanghai Universityof Finance and Economics, and published by Higher Education Press. Establishedin 2006 and with Guoqiang Tian as the Editor, the journal has a strongEditorial Advisory Board (with several Nobel Prize winners as board members),as well as a dedicated Co-Editors’ team and an Editorial Board comprised ofleading overseas and domestic Chinese economists. The FEC welcomes submissions of theoretical and empirical papers fromall fields of economics, particularly those with an emphasis on the Chineseeconomy or other transition economies.

【FEC Articles Express】

Inference for Optimal Split Point in Conditional Quantiles

Yanqin Fan, University of Washington

Ruixuan Liu, Emory University

Dongming Zhu, Shanghai University of Finance andEconomics

Abstract:

In this paper weshow the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functionsare restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree isconducted by inverting a t test or adeviation measure test, both involving Chernoff type limitingdistributions. In order to avoid estimating the nuisance parameters in thecomplicated limiting distribution, subsampling is proved to deliver the correctconfidence interval/set.

Keywords: Cubic-root Asymptotics, ChernoffDistribution, Misspecified Quantile Regression, OptimalSplit Point

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