BsplineQuantReg - 'Constrained Quantile Regression with B-Splines'

Quantile regression with B-splines under shape constraints. The initial version with cubic splines, augmented with splines of degree 1 to 4, is now able to handle all degrees (degree >= 6 without any constraint). Constraints for degrees 3 (monotone), 4 (monotone and convex) and 5 (convex) use the Karlin-Studden SOCP characterization for the sign of the polynomial (Karlin and Studden, 1966; Papp and Alizadeh, 2014), while other constraints are added as linear problems. The method for monotone constraints of cubic splines is described in Abbes (2025) <doi:10.5281/zenodo.17427913>. For quartic splines, see other references. All B-spline and polynomial functions have been rewritten for consistency. This package provides a fully independent original B-spline library for conversion between PP-form and B-spline representation, evaluation, differentiation, callable and non-callable objects, human-readable PP forms, and basis visualization, all based on De Boor's theory. It also extends to multiple knots to capture 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/>.