Publicación: CONVERGENCE ARGUMENTS TO BRIDGE CAUCHY AND MATÉRN COVARIANCE FUNCTIONS
Fecha
2023
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STATISTICAL PAPERS
Resumen
THE MATÉRN AND THE GENERALIZED CAUCHY FAMILIES OF COVARIANCE FUNCTIONS HAVE A PROMINENT ROLE IN SPATIAL STATISTICS AS WELL AS IN A WEALTH OF STATISTICAL APPLICATIONS. THE MATÉRN FAMILY IS CRUCIAL TO INDEX MEAN-SQUARE DIFFERENTIABILITY OF THE ASSOCIATED GAUSSIAN RANDOM FIELD; THE CAUCHY FAMILY IS A DECOUPLER OF THE FRACTAL DIMENSION AND HURST EFFECT FOR GAUSSIAN RANDOM FIELDS THAT ARE NOT SELF-SIMILAR. OUR EFFORT IS DEVOTED TO PROVE THAT A SCALE-DEPENDENT FAMILY OF COVARIANCE FUNCTIONS, OBTAINED AS A REPARAMETERIZATION OF THE GENERALIZED CAUCHY FAMILY, CONVERGES TO A PARTICULAR CASE OF THE MATÉRN FAMILY, PROVIDING A SOMEWHAT SURPRISING BRIDGE BETWEEN COVARIANCE MODELS WITH LIGHT TAILS AND COVARIANCE MODELS THAT ALLOW FOR LONG MEMORY EFFECT.
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Spectral densities, Random field, Positive definite, Mellin?Barnes transforms
