Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 2, 253--276

Subsampling Inference on Quantile Regression Processes

By

Victor Chernozhukov and Iv\'an Fern\'andez-Val, Massachusetts Institute of Technology, Cambridge, USA

SUMMARY. In program evaluation studies, important hypotheses concerning how a treatment or a social program affects the distribution of an outcome of interest can be tested using statistics derived from empirical conditional quantile processes. This paper develops simple and practical tests for verifying these hypotheses. The critical values for these tests are obtained by subsampling appropriately recentered empirical quantile regression processes. The resulting tests have not only good power and size properties, but also a much wider applicability than the available methods based on Khmaladzation.  Of independent interest is also the use of recentering in subsampling, which leads to substantial improvements in the finite-sample power of the tests relative to the canonical (uncentered) subsampling. This can be attributed theoretically to an improvement in  Bahadur efficiency that the recentering provides in the testing context. The new inference approach is illustrated through a reanalysis of the Pennsylvania reemployment bonus experiment.

AMS (1991) subject classification. 62-07, 62P20, 62G09, 62G10, 62M99.

Key words and phrases. Quantile regression, subsampling, Kolmogorov-Smirnov test.

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