Asymptotic inference for the constrained quantile regression process

Thomas Parker

Journal of Econometrics, 2019, vol. 213, issue 1, 174-189

Abstract: I investigate the asymptotic distribution of linear quantile regression coefficient estimates when the parameter lies on the boundary of the parameter space. In order to allow for inferences made across many conditional quantiles, I provide a uniform characterization of constrained quantile regression estimates as a stochastic process over an interval of quantile levels. To do this I pose the process of estimates as solutions to a parameterized family of constrained optimization problems, parameterized by quantile level. A uniform characterization of the dual solution to these problems – the so-called regression rankscore process – is also derived, which can be used for score-type inference in quantile regression. The asymptotic behavior of quasi-likelihood ratio, Wald and regression rankscore processes for inference when the null hypothesis asserts that the parameters lie on a boundary follows from the features of the constrained solutions.

Keywords: Quantile regression; Inequality constraints; Asymptotic inference (search for similar items in EconPapers)
JEL-codes: C12 C21 C31 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:213:y:2019:i:1:p:174-189

DOI: 10.1016/j.jeconom.2019.04.010

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