BsplineQuantReg

Constrained Quantile Regression with B-Splines (Degrees 1 to 4)

This package is available on CRAN.

Citation

If you use this package in your research, please cite:

@Article{Abbes2026,
  author  = {Alexandre Abbes},
  title   = {Constrained Quantile Regression with Cubic B-Splines under Shape Constraints},
  year    = {2026},
  doi     = {10.5281/zenodo.17427913}
}

Features

Quantile regression for any tau in (0,1)
B-splines of degree 1 to 4 (linear to quartic)
Monotonicity constraints (increasing or decreasing)
Convexity constraints (convex or concave)
Third derivative constraints for cubic and quartic splines
Karlin-Studden SOCP formulation for rigorous shape constraints
Partial constraints (per interval or per knot)
Polynomial coefficient export

Installation

From CRAN (stable, recommended)

install.packages("BsplineQuantReg")

From GitHub (development version)

# Using pak
pak::pak("alexandreabbes/BsplineQuantReg")

# Or using devtools
devtools::install_github("alexandreabbes/BsplineQuantReg")

System Requirements

Linux Users

On Linux systems, the packages CVXR and CLARABEL require the Rust compiler and Cargo package manager to be installed.

Ubuntu/Debian:

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
source ~/.cargo/env

Fedora/RHEL:

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
source ~/.cargo/env

Verify installation:

rustc --version
cargo --version

After installing Rust and Cargo, restart R and install the package:

install.packages("BsplineQuantReg")

Windows Users

Windows users do not need to install Rust separately. The package uses pre-compiled binaries available on CRAN.

R Packages

Package	Description	Constraint Type	Spline Degree
BsplineQuantReg (this package)	Quantile regression with Karlin-Studden constraints	Monotonicity, Convexity	1 to 4
quantreg	Classical quantile regression	None (linear programming)	Linear
cobs	Constrained B-splines	Monotonicity, Convexity	Linear, Quadratic

Comparison with cobs

The cobs package (Constrained B-Splines with linear or quadratic splines) is the closest to this package.

Performance Notice

This R package is intended for demonstration, prototyping, and educational purposes. Due to the current implementation (pure R with CVXR), the package is almost 5 times slower than its Python counterpart (benchmark test). B-spline quantile regression with constraints involves solving SOCP problems, and the R implementation does not yet leverage optimized linear algebra libraries.

Python version: https://pypi.org/project/BsplineQuantRegpy/

Future Improvements

Optimize the B-spline basis computation
Improve the API based on user feedback
Add a graphical User interface (GUI)

Getting Started

library(BsplineQuantReg)

# Generate sample data
set.seed(42)
x <- seq(0, 1, length.out = 100)
y <- 2*x + 0.5*sin(6*pi*x) + 0.05*rnorm(100)
knots <- quantile(x, probs = seq(0, 1, length.out = 10))

# Quantile regression with cubic spline and increasing constraint
fit <- SplineCubicQuant(x, y, knots, tau = 0.5, monot = 1)

# Evaluate the spline
x_eval <- seq(0, 1, length.out = 200)
#y_eval <- spline_eval(fit, x_eval) # deprecated now
y_eval <- fit(x_eval) # the fit is now callable

Demos

# List available demos
demo(package = "BsplineQuantReg")

# Run a specific demo
demo("comprehensive", package = "BsplineQuantReg")
demo("temperature", package = "BsplineQuantReg")

Bug Reports

Please report issues on GitHub: https://github.com/alexandreabbes/BsplineQuantReg/issues ```