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If you use this package in your research, please cite:
```bibtex @Article{Abbes2026, author = {Alexandre Abbes}, title = {Quantile regression with cubic polynomial splines under shape constraints with applications}, year = {2026}, doi = {10.5281/zenodo.17427913} }
This package is currently in beta (version 0.1.0-beta).
| Package | Description | Constraint Type | Spline Degree |
|---|---|---|---|
| ConstrainedQuantileSplines (this package) | Quantile regression with Karlin-Studden constraints | Monotonicity, Convexity | Cubic |
| quantreg | Classical quantile regression | None (linear programming) | Linear |
| cobs | Constrained B-splines | Monotonicity, Convexity | Linear, Quadratic |
The cobs package (Constrained B-Splines) is the closest
to this package, but with key differences:
| Feature | ConstrainedQuantileSplines | cobs |
|---|---|---|
| Spline degree | Cubic (degree 3) | Linear, Quadratic |
| Constraint method | Karlin-Studden SOCP | Traditional constraints |
| Convexity | ✅ Yes | ✅ Yes |
| Monotonicity | ✅ Yes | ✅ Yes |
| Quantile regression | ✅ Yes | ✅ Yes |
| Partial constraints | ✅ Yes (per interval) | Limited |
| Polynomial coefficient export | ✅ Yes | ❌ No |
cobs : For linear or quadratic
splines, simpler constraintsThis R package is currently intended for demonstration, prototyping, and educational purposes only.
Due to the current implementation (pure R with CVXR), the package is significantly slower than its Python counterpart. Cubic B-spline quantile regression with constraints involves solving SOCP problems, and the R implementation does not yet leverage optimized linear algebra libraries. Python version
Current benchmarking (median regression, n=1000, kn=20, cubic splines):
⚠️ The R version is currently 50-100x slower than Python (estimation)
We plan to improve performance in future releases by: - Linking with faster optimization libraries (OSQP, Gurobi) - Implementing more efficient SOCP solvers - Optimizing the B-spline basis computation
The Python version remains the recommended choice for production use.
pak::pak(“alexandreabbes/BsplineQuantReg”)
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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