# Fits a penalized spline with radial basis functions to data

### Description

Fits a penalized spline with radial basis functions to data.

### Usage

1 |

### Arguments

`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 |

### Details

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.

### Value

An object of class `pspline`

.

### Author(s)

Mathieu Ribatet

### References

Ruppert, D. Wand, M.P. and Carrol, R.J. (2003) *Semiparametric
Regression* Cambridge Series in Statistical and Probabilistic
Mathematics.

### See Also

`cv`

, `gcv`

### Examples

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