| lspline {assist} | R Documentation |
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 |
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 chunlei_ke@yahoo.com and Yuedong Wang yuedong@pstat.ucsb.edu
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
Examples
## Not run:
x<- seq(0,1, len=20)
lspline(x, type="exp", r=1.5)
## End(Not run)