Abstract

We consider parameter inference for linear quantile regression with non-stationary

predictors and errors, where the regression parameters are subject to inequality

constraints.

We show that the constrained quantile coefficient estimators are

asymptotically equivalent to the metric projections of the unconstrained estimator onto the constrained parameter space. Utilizing a geometry-invariant prop-

erty of this projection operation, we propose inference procedures - the Wald, likelihood ratio, and rank-based methods - that are consistent regardless of whether

the true parameters lie on the boundary of the constrained parameter space. We

also illustrate the advantages of considering the inequality constraints in analyses

through simulations and an application to an exchange rate time series.

Information

Preprint No.SS-2025-0108
Manuscript IDSS-2025-0108
Complete AuthorsYan Cui, Yuan Sun, Zhou Zhou
Corresponding AuthorsZhou Zhou
Emailszhou.zhou@utoronto.ca

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Acknowledgments

We thank Anran Jia for her contribution to an earlier version of this paper.

Supplementary Materials

The online supplementary material contains additional simulation results

and proofs of the theoretical results presented in Section 3.

Supplementary materials are available for download.