Description Usage Arguments Details Value Author(s) References See Also Examples
Return a matrix evaluating reproducing kernels for some L-splines at observed points.
1 |
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. |
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+(2π)^2, H_0=span\{sin(2π x),cos(2π x)\};
sine1: L=D(D^2+(2π)^2), H_0=span\{1, sin(2π x),cos(2π x)\};
linSinCos: L=D^4+D^2, H_0=spac\{1, x, sin(x), cos(x)\}.
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]).
Chunlei Ke chunlei\_ke@pstat.ucsb.edu and Yuedong Wang yuedong@pstat.ucsb.edu
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.
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