R: Stein nonseparable space-time model

RMstein {RandomFields} | R Documentation

## Stein nonseparable space-time model

### Description

`RMstein` is a univariate stationary covariance model whose corresponding covariance function only depends on the difference h between two points and is given by

C(h, t) = W_ν(y) - < h, z > t W_{ν-1}(y) / [ (ν-1) (2ν + d + 1) ]

Here W_ν is the covariance of the `RMwhittle` model with smoothness parameter ν; y = ||(h,t)|| is the norm of the vector (h,t), d is the dimension of the space on which the random field is considered.

### Usage

    RMstein(nu, z, var, scale, Aniso, proj)

### Arguments

`nu` | numerical value; greater than 1; smoothness parameter of the RMwhittle model
`z` | a vector; the norm of z must be less or equal to 1.
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

See Stein (2005).

### Value

`RMstein` returns an object of class `RMmodel`

### Author(s)

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

### References

- Stein, M.L. (2005) Space-time covariance functions. J. Amer. Statist. Assoc. 100, 310-321. Equation (8).

### 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 <- RMstein(nu=1.5, z=0.9)
    x <- seq(0, 10, 0.05)
    plot(RFsimulate(model, x=x, y=x))

[Package RandomFields version 3.1.50 Index]