Inference for Optimal Split Point in Conditional Quantiles

Yanqin Fan; Ruixuan Liu; Dongming Zhu

doi:10.3868/s060-005-016-0004-6

Front. Econ. China ›› 2016, Vol. 11 ›› Issue (1) : 40 -59. DOI: 10.3868/s060-005-016-0004-6

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Inference for Optimal Split Point in Conditional Quantiles

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Abstract

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 Chernoff 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.

Keywords

cubic-root asymptotics / Chernof distribution / misspecified Quantile regression / optimal split point

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Yanqin Fan, Ruixuan Liu, Dongming Zhu. Inference for Optimal Split Point in Conditional Quantiles. Front. Econ. China, 2016, 11(1): 40-59 DOI:10.3868/s060-005-016-0004-6