ncs function

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

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

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

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.

Returns

• 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.

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.

Author(s)

Luis Hernando Vanegas hvanegasp@gmail.com and Gilberto A. Paula

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