periodic: Calculate Reproducing Kernels for Periodic Polynomial Splines with Period 1
Description
Return a matrix evaluating reproducing kernels for periodic polynomial splines at observed points.
Usage
periodic(s, t=s, order=2)
Arguments
s
a numeric vector.
t
an optional vector. Default is the same as s.
order
an optional integer sepcifying the order of the polynomial spline. Default is 2 for the
periodic cubic spline.
Value
a matrix with the numbers of row and column equal to the lengths of s and t respectively.
The [i, j] element is the reproducing kernel evaluated at (s[i], t[j]).
Details
The general formula of the reproducing kernel is sum of an infinite series, which is approximated
by taking the first 50 terms. For the case of order=2, the close form is available and used.
References
Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.
Gu, C. (2001). Smoothing Spline ANOVA Modes. Chapman and Hall.