Covariance Models with Spectral Additive Components

Abstract

We present a new model defining a whole class of variogram models: the spectral additive model (SAM). The model is obtained by linear combination of simple spectral components. The SAM parameters can be estimated linearly and without bias. The handling of mean drift is straightforward. In the spatial domain, the SAM possesses an analytic expression, a clear advantage over similar approaches based on covariance spectra obtained by FFT. The SAM is flexible as it can approximate any classical model, isotropic or anisotropic, to the desired degree of precision. A forward inclusion selection procedure enables avoiding over-parameterization of the model. This is especially useful in the general anisotropic case. Simulations illustrate the performance of the SAM for covariance function fitting.