rbpspline {SpatialExtremes} | R Documentation |
Fits a penalized spline with radial basis functions to data
Description
Fits a penalized spline with radial basis functions to data.
Usage
rbpspline(y, x, knots, degree, penalty = "gcv", ...)
Arguments
y |
The response vector. |
x |
A vector/matrix giving the values of the predictor
variable(s). If |
knots |
A vector givint the coordinates of the knots. |
degree |
The degree of the penalized smoothing spline. |
penalty |
A numeric giving the penalty coefficient for the
penalization term. Alternatively, it could be either 'cv' or 'gcv'
to choose the |
... |
Details
The penalized spline with radial basis is defined by:
where are the coefficients to be estimated,
are the coordinates of the i-th knot and
where
corresponds to
the
degree
of the spline.
The fitting criterion is to minimize
where is the penalty coefficient and
the penalty matrix.
Value
An object of class pspline
.
Author(s)
Mathieu Ribatet
References
Ruppert, D. Wand, M.P. and Carrol, R.J. (2003) Semiparametric Regression Cambridge Series in Statistical and Probabilistic Mathematics.
See Also
Examples
n <- 200
x <- runif(n)
fun <- function(x) sin(3 * pi * x)
y <- fun(x) + rnorm(n, 0, sqrt(0.4))
knots <- quantile(x, prob = 1:(n/4) / (n/4 + 1))
fitted <- rbpspline(y, x, knots = knots, degree = 3)
fitted
plot(x, y)
lines(fitted, col = 2)