Journal
STATISTICS & PROBABILITY LETTERS
Volume 83, Issue 3, Pages 850-855Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.spl.2012.12.009
Keywords
Correlation function; Hausdorff dimension; Moving average; Power kernel; Random field
Categories
Funding
- Centre for Stochastic Geometry and Advanced Bioimaging at Aarhus University
- Villum Foundation
- German Research Foundation (DFG) within the program Spatio-/Temporal Graphical Models and Applications in Image Analysis [GRK 1653]
- SFI2, Statistics for Innovation, Oslo
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The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matern covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Levy basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result, the model offers similar flexibility in the fractal properties of the resulting field as the Matern model. (C) 2012 Elsevier B.V. All rights reserved.
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