R: Estimates the penalty coefficient from the cross-validation...

cv {SpatialExtremes} | R Documentation

## Estimates the penalty coefficient from the cross-validation criterion

### Description

Estimates the penalty coefficient from the cross-validation criterion.

### Usage

    cv(y, x, knots, degree, plot = TRUE, n.points = 150, ...)

### Arguments

`y` | The response vector.
`x` | A vector/matrix giving the values of the predictor variable(s). If `x` is a matrix, each row corresponds to one observation.
`knots` | A vector givint the coordinates of the knots.
`degree` | The degree of the penalized smoothing spline.
`plot` | Logical. If `TRUE` (default), the evolution of the CV score as the penalty increases is plotted.
`n.points` | A numeric giving the number of CV computations needed to produce the plot.
`...` | Options to be passed to the `nlm` function.

### 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

    n <- 200
    x <- runif(n)
    fun <- function(x) sin(3 * pi * x)
    y <- fun(x) + rnorm(n, 0, sqrt(0.4))
    knots <- quantile(x, prob = 1:(n/4) / (n/4 + 1))
    cv(y, x, knots = knots, degree = 3)

[Package SpatialExtremes version 2.0-5 Index]