cov.askey {GeneralizedWendland}

Askey covariance function

Description

A covariance function of the form

\rho_{\beta,\kappa,\mu} = \begin{cases} \sigma + \theta \quad 0 \leq r < \epsilon \\ (1-r)^{\mu} \quad \epsilon \leq r < 1 \\ 0 \quad 1 \leq r \end{cases}

where r=h/\beta. This is equivalent to the generalized Wendland covariance with \kappa=0, but much more computationally efficient.

Usage

cov.askey(h, theta, ..., cov.args = list())

Arguments

h

A numeric vector, matrix, or spam object storing distances.

theta

Numeric vector \vec{\theta}=(\beta, \sigma, \mu, \theta) storing parameters.

...

Other arguments.

cov.args

Named list of arguments. See Details.

Details

Using the list cov.args, users can provide the following arguments:

cov.eps (default: .Machine$double.eps^0.5)

The threshold distance \epsilon below which the function will return \sigma + \theta.

Value

Returns an object of the same type as input object h which stores the computed covariance values, i.e. a spam object if input h was also a spam object.

Author(s)

Thomas Caspar Fischer

References

Moreno Bevilacqua and Tarik Faouzi and Reinhard Furrer and Emilio Porcu (2019) Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics, Annals of Statistics, 47(2), 828–856.

See Also

cov.wendland