lspline: Calculate Reproducing Kernels for Some L-splines

In assist: A Suite of R Functions Implementing Spline Smoothing Techniques

Calculate Reproducing Kernels for Some L-splines

Description

Return a matrix evaluating reproducing kernels for some L-splines at observed points.

Usage

lspline(x,y=x, type="exp", ...)

Arguments

x	a numeric vector on which reproducing kerenls are evaluated.
y	an optional vector, specifying the second argument of reproducing kernels. Default is x.
type	a string indicating the type of L-splines. Available options are "exp", "logit","sine", "sine1", and "linSinCos". Default is "exp".
...	other arguments needed.

Details

Denote L as the differential oprator, H_0 as the null (kernel) space. The available kernels correspond to the following L:

• exp: L=rD+D^2, H_0=span\{1,exp(-rx)\}. r>0, default to be 1;
  

• logit: L=D-1/(1+e^t), H_0=span\{e^t/(1+e^t)\};
  

• sine0: L=D^2+(2\pi)^2, H_0=span\{sin(2\pi x),cos(2\pi x)\};
  

• sine1: L=D(D^2+(2\pi)^2), H_0=span\{1, sin(2\pi x),cos(2\pi x)\};
  

• linSinCos: L=D^4+D^2, H_0=spac\{1, x, sin(x), cos(x)\}.

Value

a matrix with the numbers of row and column equal to the lengths of x and y respectively. The [i, j] element is the reproducing kernel evaluated at (x[i], y[j]).

Author(s)

Chunlei Ke [e-mail] and Yuedong Wang [e-mail]

References

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.

Heckman, N and Ramsay, J. O. (2000). Penalised regression with model-based penalties. To appear in Canadian Journal of Statisitcs.

See Also

ssr

Examples

## Not run: 
x<- seq(0,1, len=20)
lspline(x, type="exp", r=1.5)

## End(Not run)

assist documentation built on Aug. 22, 2023, 9:12 a.m.