Quantile Regression with Smoothing Splines

This function is used to fit a quantile smoothing spline with L2 penalty.

Usage

qsmspline(x, y, p, lambda = 1, maxIter = 300, eps = 1e-2, gamma = 10,
  aggressive = FALSE)

Arguments

x,y: vectors giving the coordinates of the points to be interpolated.
p: quantile to be estimated.
lambda: penalty parameter.
maxIter: the maximum number of iterations.
eps: the absolute convergence tolerance.
gamma: scaling for initial values.
aggressive: aggressive step size in Bosch et al (1995) - not yet implemented.

Details

This is an implementation of Bosch et al's (1995) algorithm to fit a quantile smoothing spline with L2 penalty. The penalty parameter must be set by the user.

Value

a list containing the following components (see Bosch et al, 1995)

a1: first set of constraints.
a2: second set of constraints.
b1: Lagrangian associated with a1.
b2: Lagrangian associated with a2.
fit: fitted values.

References

Bosch RJ, Ye Y, and Woodworth GG. A convergent algorithm for quantile regression with smoothing splines. Computational Statistics and Data Analysis. 1995;19(6):613-30.

Author

Marco Geraci

Examples

# Generate data
set.seed(123)
n <- 100
x <- sort(runif(n, 0, 2*pi))
y <- sin(x) + (1 + x)*rnorm(n, 0, 0.1)

# Fit median - lambda set at an arbitrary value
fit <- qsmspline(x = x, y = y, p = 0.5, lambda = 0.1)

# Plot
plot(x, y)
lines(x, fit[['fit']])