ssym (version 1.1)

ncs.graph: Tool for plotting a natural cubic spline

Description

ncs.graph is used to find the value of the natural cubic spline f(t) at any point t, and hence to plot a graph of f(t) to any desired degree of accuracy.

Usage

ncs.graph(x,g,gam,cont)

Arguments

x

knots of the natural cubic spline, it is a set (ordered ascending) formed by the different values of t in the sample.

g

a vector with the estimates of f(t) for all t in x.

gam

a vector with the second derivative of f(t) for all t in x.

cont

a positive integer, which indicates the degree of accuracy to plot a graph of f(t).

Value

• pg
  a matrix with two columns representing an ordered set of pairs (t,f(t)) to plot a graph of f(t) to desired degree of accuracy.

References

Green, P.J. and Silverman, B.W. (1994) Nonparametric Regression and Generalized Linear Models, Boca Raton: Chapman and Hall.

Examples

m1 <- "Estimated NCS for different values of the smoothing parameter (k)"
n <- 300
t <- round(runif(n),digits=2)
y <- cos(4*pi*t) + rnorm(n)
ss <- splinek(as.numeric(levels(factor(t))),t)
N <- ss$N
M <- ss$K
lambda <- c(0.002,0.02,0.2,2,20)
plot(t,y,xlim=range(t),ylim=range(y),cex=0.3,lwd=3,xlab="",ylab="",main=m1)
for(i in 1:length(lambda)){
	h <- solve(t(N)%*%N + lambda[i]*M)%*%t(N)%*%y
	gam <- solve(ss$R)%*%t(ss$Q)%*%h
	sa <- ncs.graph(as.numeric(levels(factor(t))),h,gam,1000)
	par(new=TRUE)
	plot(sa[,1],sa[,2],xlim=range(t),ylim=range(y),type="l",xlab="t",ylab="",col=i)
}
legend(min(t),max(y),bty="n",col=1:length(lambda),legend=paste("k = ",lambda),lty=1)