Quantile planes without crossing via nonlinear programming

Background and objective: In this note we propose a nonlinear programming approach for simultaneous fitting of quantile regression models for two or more quantiles. The approach is straightforward, flexible and practical. We apply this approach to a dataset of lactic acid values from a screening dataset in childhood malaria. Methods: We carry out the fitting of simultaneous quantile regression models using a specific definition of a quantile as an expectation via nonlinear programming methods given certain monotonicity constraints. Results: We illustrate through simulations and examples that are new approach to simultaneous quantile regression is practical and feasible. The approach is supplemented by providing a bootstrap framework for confidence interval estimation. Conclusions: Our nonlinear programming approach towards solving the simultaneous quantile regression fitting is shown to be a practical approach that should appeal to statistical practitioners.