Valid covariance estimation under stationarity
- García Soidán, Pilar
- Menezes, Raquel
Publisher: Comité organizador del XXX Congreso Nacional de Estadística e Investigación Operativa y IV Jornadas de Estadística Pública
ISBN: 978-84-690-7249-3
Year of publication: 2007
Congress: Congreso Nacional de Estadística e Investigación Operativa (30. 2007. Valladolid)
Type: Conference paper
Abstract
Estimation of the second-order structure plays a crucial role for spatial prediction, since the kriging equations may be expressed in terms of the variogram or the covariance function which are, in general, unknown. In this work, the series expansion approach is considered for estimation of the covariance function. The choice of a smoothing parameter is necessary, related to the number of terms to be considered in the series, which will be selected by minimizing the corresponding mean integrated squarederror. A remarkable advantage of this approach is that, under appropriate conditions, it can also be used for transformation of a given covariance estimator into a valid one, which satisfies the semi-definiteness property.