Nonstandard
Quantile-Regression Inference
(with Keith Knight)
Econometric Theory 25(5): 1415-1432, 2009.
Abstract
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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. |
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KEYWORDS: Quantile regression,
hypothesis testing, bandwidth selection |
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