R: Nugget Effect Covariance Model

RMnugget {RandomFields} | R Documentation

## Nugget Effect Covariance Model

### Description

`RMnugget` is a multivariate stationary isotropic covariance model called “nugget effect”. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given for i,j in 1,...,`vdim` by

C_{ij}(r) = δ_ij 1_{0}(r),

where δ_{ij}=1 if i=j and δ_{ij}=0 otherwise.

### Usage

    RMnugget(tol, vdim, var, scale, Aniso, proj)

### Arguments

`tol` | Only for advanced users. See `RPnugget`.
`vdim` | Only for advanced users. See `RPnugget`.
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

Note that the argument `scale` does not affect the covariance model; `Aniso` has an effect in case of zonal anisotropy.

The nugget effect belongs to Gaussian white noise and is often used for modeling measurement errors.

The locations at a distance less than or equal to `nugget.tol` are considered as being identical. This strategy applies to the simulation method and the covariance function itself. Hence, the covariance function is only positive definite if `nugget.tol=0.0`. However, if the anisotropy matrix does not have full rank and `nugget.tol=0.0` then, the simulations are likely to be odd. The value of `nugget.tol` should be of order 1e-15.

### Value

`RMnugget` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### See Also

`RMmodel`, `RFsimulate`, `RFfit`.

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    model <- RMnugget(Aniso=matrix(1, nr=2, nc=2))
    x <- seq(0, 10, 0.02)
    plot(RFsimulate(model, x=x, y=x, tol=1e-10))

[Package RandomFields version 3.1.50 Index]