ssym (version 1.5.7)

ncs: Tool to build the basis matrix and the penalty matrix of natural cubic splines.

Description

ncs builds the basis matrix and the penalty matrix to approximate a smooth function using a natural cubic spline.

Usage

ncs(xx, lambda, nknots, all.knots)

Value

xx

the explanatory variable \(xx\) with the following attributes: set of knots, basis matrix, penalty matrix, smoothing parameter (if it was specified), and other interest matrices.

Arguments

xx

the explanatory variable.

lambda

an optional positive value that represents the smoothing parameter value.

nknots

an optional positive integer that represents the number of knots of the natural cubic spline. Default is \(m=[n^{\frac{1}{3}}]+3\). The knots are located at the quantiles of order \(0/(m-1),1/(m-1),\ldots,(m-1)/(m-1)\) of xx.

all.knots

logical. If TRUE, the set of knots and the set of different values of \(xx\) coincide. Default is FALSE.

Author

Luis Hernando Vanegas <[e-mail]> and Gilberto A. Paula

References

Lancaster, P. and Salkauskas, K. (1986) Curve and Surface Fitting: an introduction. Academic Press, London. Green, P.J. and Silverman, B.W. (1994) Nonparametric Regression and Generalized Linear Models, Boca Raton: Chapman and Hall.

Examples

n <- 300
t <- sort(round(runif(n),digits=1))

t2 <- ncs(t,all.knots=TRUE)
N <- attr(t2, "N") ## Basis Matrix
M <- attr(t2, "K") ## Penalty Matrix
knots <- attr(t2, "knots") ## Set of knots