Nonparametric Testing of an Exclusion Restriction in Quantile Regression

Abstract

Using the framework proposed by Bickel et al. (2006), we provide a score-based testing method to check the exclusion restriction in quantile regression, i.e., H: ν_α(Y|U, V) = ν_α(Y|U) w.p.1, where ν_α denotes the αth (0 < α < 1) quantile. A subsampling method is suggested to acquire the critical values and justified. The tests are all found to be consistent against fixed alternatives and have discriminating power against local alternatives at root-n scale. We address this particular problem as a representative among a wide family of semiparametric model checking problems. The methodology can be carried over to other goodness-of-fit testing of semiparametric models, possibly involve non smooth functions.

Keywords:

• Empirical processes
• Hypothesis testing
• Quantile regression
• Semiparametric

Mathematics Subject Classification:

• Primary 62G10
• Secondary 62G20

Acknowledgment

The author is grateful for Prof. Peter J. Bickel and Prof. James Powell for their suggestions and communications. Thanks also to the Associate Editor and the two referees for their comments. This work was partly supported by the National Natural Science Foundation of China (70621061) and Tsinghua University Grant for Young Researchers.