Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 2, 187--199

Isotonic Quantile Regression: Asymptotics and Bootstrap

By

Jason Abrevaya, Purdue University, W.\ Lafayette, IN, USA

SUMMARY. This paper considers a nonparametric model in which (i)~the conditional quantile function is assumed to be nondecreasing and (ii)~the distribution of the error disturbance may depend upon the covariate. For this general model, the (pointwise) limiting distribution of the isotonic quantile regression estimator (Casady and Cryer~(1976)) is derived. Since the bootstrap is not consistent for this estimator, an adjusted version of the bootstrap is discussed as an alternative method for inference. An empirical application to birthweights is considered.

AMS (1991) subject classification. 62G08, 62G09, 62G20.

Key words and phrases. Isotonic quantile regression, cube-root asymptotics, bootstrap.

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