Premium
On the Estimation of Integrated Covariance Functions of Stationary Random Fields
Author(s) -
PANTLE URSA,
SCHMIDT VOLKER,
SPODAREV EVGENY
Publication year - 2010
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2009.00663.x
Subject(s) - mathematics , law of total covariance , random field , covariance function , multivariate random variable , covariance , estimator , covariance matrix , estimation of covariance matrices , matérn covariance function , covariance mapping , rational quadratic covariance function , gaussian , gaussian random field , statistics , gaussian process , covariance intersection , random variable , physics , quantum mechanics
. For stationary vector‐valued random fields on the asymptotic covariance matrix for estimators of the mean vector can be given by integrated covariance functions. To construct asymptotic confidence intervals and significance tests for the mean vector, non‐parametric estimators of these integrated covariance functions are required. Integrability conditions are derived under which the estimators of the covariance matrix are mean‐square consistent. For random fields induced by stationary Boolean models with convex grains, these conditions are expressed by sufficient assumptions on the grain distribution. Performance issues are discussed by means of numerical examples for Gaussian random fields and the intrinsic volume densities of planar Boolean models with uniformly bounded grains.