a1 University of Toronto
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.
Goh’s research was partially supported by the Connaught Fund of the University of Toronto. Knight’s research was supported by the Natural Sciences and Engineering Research Council of Canada. Both authors are grateful to Paolo Paruolo and to two referees for their helpful comments.