Fits a penalized spline with radial basis functions to data.
1 |
y |
The response vector. |
x |
A vector/matrix giving the values of the predictor
variable(s). If |
knots |
A vector givint the coordinates of the knots. |
degree |
The degree of the penalized smoothing spline. |
penalty |
A numeric giving the penalty coefficient for the
penalization term. Alternatively, it could be either 'cv' or 'gcv'
to choose the |
... |
Additional options to be passed to the |
The penalized spline with radial basis is defined by:
f(x) = β_0 + β_1 x + … + β_{m-1} x^{m-1} + ∑_{k=0}^{K-1} β_{m+k} || x - κ_k ||^{2m - 1}
where β_i are the coefficients to be estimated,
κ_i are the coordinates of the i-th knot and
m = (d+1)/2 where d corresponds to
the degree
of the spline.
The fitting criterion is to minimize
||y - X β||^2 + λ^{2m-1} β^T K β
where λ is the penalty coefficient and K the penalty matrix.
An object of class pspline
.
Mathieu Ribatet
Ruppert, D. Wand, M.P. and Carrol, R.J. (2003) Semiparametric Regression Cambridge Series in Statistical and Probabilistic Mathematics.
cv
, gcv
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Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
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