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NONSTANDARD QUANTILE-REGRESSION INFERENCE

Published online by Cambridge University Press:  01 October 2009

S.C. Goh*
Affiliation:
University of Toronto
K. Knight
Affiliation:
University of Toronto
*
*Address correspondence to S.C. Goh, Department of Economics, University of Toronto, Max Gluskin House, 150 St. George Street, Toronto, Ontario, Canada M5S 3G7; e-mail: goh@economics.utoronto.ca.

Abstract

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.

Type
NOTES AND PROBLEMS
Copyright
Copyright © Cambridge University Press 2009

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