Quantile planes without crossing via nonlinear programming
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1Roswell Park Cancer Institute, Department of Biostatistics and Bioinformatics, Elm and Carlton Streets, Buffalo, NY 14623, United States.
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.
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