Nonstandard Quantile-Regression Inference

18 Pages Posted: 21 May 2007 Last revised: 4 Sep 2009

See all articles by Chuan Goh

Chuan Goh

University of Guelph

Keith Knight

University of Toronto - Department of Statistics


It is well-known that conventional Wald-type inference in the context of quantile regression is complicated by the need to construct estimates of the conditional densities of the response variables at the quantile of interest. This note explores the possibility of circumventing the need to construct conditional density estimates in this context with scale statistics that are explicitly inconsistent for the underlying conditional densities. This method of Studentization leads conventional test statistics to have limiting distributions that are nonstandard but have the convenient feature of depending explicitly on the user's choice of smoothing parameter. These limiting distributions depend on the distribution of the conditioning variables but can be straightforwardly approximated by resampling.

Keywords: Quantile regression, hypothesis testing, bandwidth selection

JEL Classification: C12, C14, C21, C29

Suggested Citation

Goh, Chuan and Knight, Keith, Nonstandard Quantile-Regression Inference. Econometric Theory, Vol. 25, No. 5, pp. 1415-1432, 2009, Available at SSRN: or

Chuan Goh (Contact Author)

University of Guelph

Department of Economics and Finance
University of Guelph, 50 Stone Road East
Guelph, Ontario

Keith Knight

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3

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