Package {BsplineQuantReg}

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Description

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Usage

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Build B-spline basis in piecewise polynomial form Computes local polynomial coefficients for each B-spline basis function on each interval. Polynomials are expressed in the canonical basis Uses De Boor's recursion formula.

Description

Build B-spline basis in piecewise polynomial form Computes local polynomial coefficients for each B-spline basis function on each interval. Polynomials are expressed in the canonical basis Uses De Boor's recursion formula.

Usage

Bspline_base(sn, degree = 3, der = 0, verbose = FALSE)

Arguments

Value

A list containing:

Examples

sn <- c(0,0,0,0,1,2,3,4,5,5,5,5)
basis <- Bspline_base(sn, degree=3)
x=(0:(5*100))/100
y=bs_direct(basis,x)
matplot(x,t(y))
#or simple:
#view_basis(basis)

Differentiate a B-spline basis

Description

Computes the basis of order der derivatives of a B-spline basis.

Usage

Bspline_deriv(bspline, der = 2, verbose = FALSE)

Arguments

Value

A list similar to Bspline_base for the derivative basis

Omega function for De Boor recursion

Description

Computes the affine element used in the recursive De Boor algorithm for B-spline construction. for a given extended knots partition s(1),.. Omega(j,l)(x)=(s(j-x))/(s(j+l-1)-s(j)\), with l: order of the spline

Usage

Omega(s, j, o)

Arguments

Value

(Side function) A Vector of coefficients [alpha, beta] representing (alpha*t + beta)

Constrained quantile regression with cubic splines

Description

Performs quantile regression using cubic B-splines, with optional monotonicity constraints (via Karlin-Studden) and convexity constraints.

Usage

SplineConstQuantRegBs3(
  xtab,
  ytab,
  knots,
  tau,
  monot = 0,
  convcons = 0,
  solver = "CLARABEL",
  weight = NULL,
  verbose = FALSE
)

Arguments

Value

A list containing:

References

• Abbes, A. (2025). Quantile regression with cubic polynomial splines under shape constraints with applications . Zenodo. doi:10.5281/zenodo.16999784

• de Boor, C. (1978). A Practical Guide to Splines. Springer-Verlag. doi:10.1007/978-1-4612-6333-3

• Karlin, S., & Studden, W. J. (1966). Tchebycheff Systems: With Applications in Analysis and Statistics. Interscience.

• Koenker, R., & Bassett, G. (1978). Regression Quantiles. Econometrica, 46(1), 33-50. doi:10.2307/1913643

• Koenker, R. (2025). quantreg: Quantile Regression. R package version 5.99. https://CRAN.R-project.org/package=quantreg

• Ng, P., & Maechler, M. (2024). cobs: Constrained B-Splines. R package version 1.3-8. https://CRAN.R-project.org/package=cobs

See Also

Related R packages:

• quantreg - Quantile regression with linear programming

• cobs - Constrained B-sines (linear and quadratic only)

Other implementations:

• MATLAB/Python versions: https://github.com/alexandreabbes/Constrained-Quantile-Regression-with-cubic-splines

Examples

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

# Median quantile regression without constraints
fit <- SplineConstQuantRegBs3(x, y, knots, tau=0.5)

# With increasing monotonicity constraint
fit_monot <- SplineConstQuantRegBs3(x, y, knots, tau=0.5, monot=1)

# With convexity constraint
fit_convex <- SplineConstQuantRegBs3(x, y, knots, tau=0.5, convcons=1)

Derivatives at knots of a B-spline

Description

Computes derivative values of a B-spline at knots (efficient because it directly uses polynomial coefficients).

Usage

Spline_der_knots(Bspline, der = 1)

Arguments

Value

Matrix of derivative values (n_splines x n_knots)

Karlin-Studden constraints for positivity

Description

Applies Karlin-Studden SOCP constraints to ensure positivity of a quadratic polynomial on the interval [0,1].

Usage

apply_karlin_constraints(p2, p1, p0, z0, verbose = FALSE)

Arguments

Value

List of CVXR constraints

Direct evaluation of a B-spline basis

Description

Computes the values of all B-spline basis functions at given points.

Usage

bs_direct(Basis, xvalues)

Arguments

Value

Matrix of basis function values (n_splines x length(xvalues))

Convert B-spline to derivative coefficients

Description

Converts a B-spline basis to normalized first and second derivative coefficients on each interval.

Usage

bspline_to_deriv_coeffs_pp(tn, degree = 3, xvalues = 0, verbose = FALSE)

Arguments

Value

A list containing:

Change polynomial basis (Taylor expansion)

Description

Converts a polynomial expressed in the basis (t-a)^k to its representation in the basis (t-b)^k using Taylor's formula. P(t) = sum c_k (t-a)^k P(t) = sum c"_k (t-b)^k

Usage

change_polynomial_base_taylor(coeffs_a, a, b)

Arguments

Value

Coefficients in basis centered at b

Evaluate a piecewise polynomial (PP) form

Description

Evaluates a piecewise polynomial function at given points.

Usage

evalpp(p, xvalues)

Arguments

Value

Function values at the requested points

Check if package is beta version

Description

Check if package is beta version

Usage

is_beta()

Value

TRUE if beta version

Build a piecewise polynomial (PP) form

Description

Creates a PP structure from polynomial coefficients and knots.

Usage

makpp(coef, tn)

Arguments

Value

List with components coefficients and knots

Get package version

Description

Get package version

Usage

package_version()

Value

Current version string

Evaluate polynomial

Description

Evaluates a polynomial at one or more points.

Usage

poly_eval(p, xvalues)

Arguments

Value

Vector of same length as xvalues : polynomial values at the points xvalues

Examples

# P(x) = 1 + x + x^2
poly_eval(c(1, 1, 1), c(0, 1, 2)) # returns c(1, 3, 7)

Polynomial addition

Description

Adds two polynomials represented by coefficients in decreasing power order.

Usage

polyadd(p1, p2, verbose = FALSE)

Arguments

Value

Coefficient vector of the sum

Examples

polyadd(c(1, 1), c(1, -1)) # returns c(2, 0)

Polynomial derivative Computes the derivative of order der of a polynomial.

Description

Polynomial derivative Computes the derivative of order der of a polynomial.

Usage

polyderiv(p, der = 1)

Arguments

Value

Coefficients of the derivative polynomial

Examples

# P(x) = x^2 -> P'(x) = 2x
polyderiv(c(1, 0, 0), 1) # returns c(2, 0)

Polynomial multiplication

Description

Multiplies two polynomials represented by coefficients in decreasing power order.

Usage

polymul(p1, p2, ord = 0, verbose = FALSE)

Arguments

Value

Coefficient vector of the product polynomial (decreasing powers)

Examples

# (1 + x) * (1 + x) = 1 + 2x + x^2
polymul(c(1, 1), c(1, 1)) # returns c(1, 2, 1)

Reduce polynomial

Description

Removes leading zeros from a polynomial coefficient vector.

Usage

reduce_pol(p, verbose = FALSE)

Arguments

Value

Reduced vector (without leading zeros)

Examples

reduce_pol(c(0,0, 1, 1))

Evaluate a B-spline

Description

Evaluates a spline (linear combination of B-splines) at given points.

Usage

spline_eval(Bspline, xvalues)

Arguments

Value

vector of same length as xvalues, with Spline values at the requested points

Examples

{ # Create and evaluate a spline
sn <- c(0,0,0,0,1,2,3,4,5,5,5,5)
basis <- Bspline_base(sn, degree=3)
basis$coefficients <- runif(basis$n_splines)
y <- spline_eval(basis, seq(0,5,length=100))}

Comprehensive test function

Description

Runs quantile regression tests with and without constraints, and displays results. Demo function.

Usage

test_karlin_simple(verbose = FALSE, seed = NULL)

Arguments

Value

No return value, produces plots.

Examples

test_karlin_simple()

Visualize a B-spline functions basis

Description

Plots all functions of a B-spline basis.

Usage

view_basis(Bspline, xvalues = 0)

Arguments

Value

No return value, called for side effects (generates a plot)