BsplineQuantReg - 'Constrained Quantile Regression with B-Splines'

Quantile regression with B-splines under shape constraints. The initial version with cubic splines is now augmented with splines of degree 1 to 4. Constraints for degrees 3 (monotone) and 4 (monotone and convex) use the Karlin-Studden SOCP characterization for the sign of the polynomial, while other constraints applied at the knots are added as linear problems. The method for cubic splines is described in 'Abbes (2025)' <doi:10.5281/zenodo.17427913>. Other formulations are simple consequences of the other given references. All B-spline and polynomial functions have been rewritten for consistency. This package provides an original B-spline library for conversion between PP-form and B-spline representation, evaluation, differentiation, callable and non-callable objects, print human readable pp forms, view basis, all based on "De Boor\'s" theory. It also extends to multiple knots to catch up singularities. This feature is robust in the package including for constrained regression. This R implementation is intended for demonstration and prototyping. An equivalent Python package is available at <https://pypi.org/project/BsplineQuantRegpy/>.