# Estimates the penalty coefficient from the cross-validation criterion

### Description

Estimates the penalty coefficient from the cross-validation criterion.

### 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. |

`plot` |
Logical. If |

`n.points` |
A numeric giving the number of CV computations needed to produce the plot. |

`...` |
Options to be passed to the |

### Details

For every linear smoother e.g. *y.hat =
S_λ y*, the cross-validation criterion consists in minimizing
the following quantity:

*CV(λ) = ∑_{i=1}^n [(y_i - y.hat_i)
/ (1 - S_{λ,ii}) ]^2*

where *λ* is the penalty coefficient, *n* the
number of observations and *S_{λ,ii}* the
i-th diagonal element of the matrix *S_λ*.

### Value

A list with components 'penalty', 'cv' and 'nlm.code' which give the
location of the minimum, the value of the cross-validation
criterion at that point and the code returned by the `nlm`

function - useful to assess for convergence issues.

### 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`

### Examples

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