Statistical tests of heterogeneity for anisotropic multifractional Brownian fields
In this paper, we deal with some anisotropic extensions of the multifractional Brownian fields that account for spatial phenomena whose properties of regularity and directionality may both vary in space. Our aim is to set statistical tests to decide whether an observed field of this kind is heteroge...
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| Veröffentlicht in: | Stochastic processes and their applications 2020-08, Vol.130 (8), p.4667-4692 |
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| creator | Vu, Huong T.L. Richard, Frédéric J.P. |
| description | In this paper, we deal with some anisotropic extensions of the multifractional Brownian fields that account for spatial phenomena whose properties of regularity and directionality may both vary in space. Our aim is to set statistical tests to decide whether an observed field of this kind is heterogeneous or not. The statistical methodology relies upon a field analysis by quadratic variations, which are averages of square field increments. Specific to our approach, these variations are computed locally in several directions. We establish an asymptotic result showing a linear Gaussian relationship between these variations and parameters related to regularity and directional properties of the model. Using this result, we then design a test procedure based on Fisher statistics of linear Gaussian models. Eventually we evaluate this procedure on simulated data. |
| doi_str_mv | 10.1016/j.spa.2020.01.012 |
| format | Article |
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Our aim is to set statistical tests to decide whether an observed field of this kind is heterogeneous or not. The statistical methodology relies upon a field analysis by quadratic variations, which are averages of square field increments. Specific to our approach, these variations are computed locally in several directions. We establish an asymptotic result showing a linear Gaussian relationship between these variations and parameters related to regularity and directional properties of the model. Using this result, we then design a test procedure based on Fisher statistics of linear Gaussian models. 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| subjects | Anisotropic fractional Brownian field Anisotropy Applications Engineering Sciences Heterogeneity Methodology Multifractional Brownian field Quadratic variations Signal and Image processing Statistical test Statistics Statistics Theory |
| title | Statistical tests of heterogeneity for anisotropic multifractional Brownian fields |
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