Introduction

Simple example

 n_points <- 50
  xtab = ((0:(n_points)) / (n_points))

  # simple pscillating data
  #ytab<- -3 * xtab +sin(3*2*xtab*3.14)+ 0.2 * rnorm(n_points+1)
  #ytab= <- 2* xtab + 0.5 * sin(6 * pi * xtab) + 0.1 * rnorm(n_points+1)
  ytab <- xtab * (1 - xtab) + 0.1 * rnorm(n_points + 1)
  kn <- 8

  n = 7

  monot1 = c(rep(1, n), rep(0, (12 - n)))
  monot2 = rep(1,12)
  knot <- ((0:(kn + 5)) / (kn + 5))
  
  res <- quantile_spline(
    xtab = xtab,
    ytab = ytab,
    knot,
    tau = 0.5,
    monot = 0,
    degree = 3,
    verbose = FALSE
  )
 res_part_croissant <- quantile_spline(
    xtab = xtab,
    ytab = ytab,
    knot = knot,
    tau = 0.5,
    degree = 3,
    monot = monot1,
    convcons = 0,
    verbose = FALSE
  )
#> Not enough monotonicity constraints, completing with 0
 
 res_croissant <- quantile_spline(
    xtab = xtab,
    ytab = ytab,
    knot = knot,
    tau = 0.5,
    degree = 3,
    monot = 1,
    convcons = 0,
    verbose = FALSE
  )
 
 
par(mfrow = c(1, 3))
x_eval=(0:200)/200
  y_sans = spline_eval(res, x_eval)
  y_part_croiss = spline_eval(res_part_croissant, x_eval)
  y_croiss = spline_eval(res_croissant, x_eval)
  
    plot(
    xtab,
    ytab,
    pch = 16,
    cex = 0.5,
    col = "black",
    main = c("Without constraint")
    )
    lines(x_eval, y_sans, lwd = 2)  
    
  plot(
    xtab,
    ytab,
    pch = 16,
    cex = 0.5,
    col = "black",
    main = c("Mixed mootone :\n global increasing constraints
                "
    )
  )
  lines(x_eval, y_croiss, lwd = 2)  

    
    plot(
    xtab,
    ytab,
    pch = 16,
    cex = 0.5,
    col = "black",
    main = c("Mixed mootone :\n increasing constraints
                \n on the first inter-knots"
    )
  )
  lines(x_eval, y_part_croiss, lwd = 2)  

Core content

The initial version with cubic splines is now augmented with splines of degree 0 to 4 for constrained regression, and any degree for regression without monotone constraints.

• Demo degrees_comparison — simultaneous comparison of constraints across degrees 1, 2, 3, and 4.

Constraints for degree 3 (monotone), degree 4 (monotone and convex) and degree 5 (convex) use the Karlin–Studden SOCP characterization.

• Vignettes theoretical_background, shape_constraints
• Demos
  • monotonicity_basic — monotonicity constraints
  • convexity — convexity and concavity constraints
  • temperature — temperature anomaly analysis: uniform increasing vs mixed constraints (decreasing 1956–1973 only)
  • temperature2 — temperature anomaly analysis with alternative constraint configurations
  • logistic — quantile regression test on a logistic function
  • comprehensive — comprehensive test of various constraints on an oscillating function

Third-derivative constraints are supported for degrees 3 and 4.

• Demo demo_der3 — demonstration of third-order derivative constraints.

B-spline library

All B-spline and polynomial functions have been rewritten for consistency. The package provides an original B-spline library for:

• conversion between PP-form and B-spline representation,
• evaluation and differentiation,
• callable and non-callable objects,
• printing human-readable pp forms,
• viewing the basis,

all based on De Boor’s theory.

• Vignettes polynomial_library, bspline_basis_manipulation

Differentiation of B-splines can be performed either on the spline (polynomial differentiation) or on the basis.

• Demo derivative2 — coherence of the derivative functions.

The library also extends to multiple knots to handle singularities, robustly, including for constrained regression.

• Demos
  • shock — regression with discontinuity and derivability singularity
  • shock_basis — same as shock, with singular B-spline basis display

Graphical user interface

# From CRAN:
# install.packages("BsplineQuantRegGui")

# Or from GitHub:
# install.packages("remotes")
# remotes::install_github("<user>/BsplineQuantRegGUI")

# Launch:
# BsplineQuantRegGui::run_app()