dot-cor_fs function

Calculate correlation for fully symmetric model

.cor_fs(nugget, c, gamma = 1/2, a, alpha, beta = 0, h, u)

Arguments

• nugget: The nugget effect $\in[0, 1]$.
• c: Scale parameter of cor_exp, $c>0$.
• gamma: Smooth parameter of cor_exp, $\gamma\in(0, 1/2]$.
• a: Scale parameter of cor_cauchy, $a>0$.
• alpha: Smooth parameter of cor_cauchy, $\alpha\in(0, 1]$.
• beta: Interaction parameter, $\beta\in[0, 1]$.
• h: Euclidean distance matrix or array.
• u: Time lag, same dimension as h.

Returns

Correlations of the same dimension as h and u.

Details

The fully symmetric correlation function with interaction parameter $\beta$ has the form

where $\|\cdot\|$ is the Euclidean distance, and $\delta_{x=0}$ is 1 when $x=0$ and 0 otherwise. Here $\mathbf{h}\in\mathbb{R}^2$ and $u\in\mathbb{R}$. By default beta = 0 and it reduces to the separable model.

References

Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space–Time Data, Journal of the American Statistical Association, 97:458, 590-600.