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Consider a stationary Gaussian random field on R d with spectral density f (λ) that satisfies f (λ) ∼ c |λ| −θ as |λ| → ∞. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data observed on a grid, we propose estimators of c and θ by minimizing an… (More)

Consider a stationary Gaussian random field on R d with the spectral density f (λ) that satisfies f (λ) ∼ c |Hλ| −θ as |λ| → ∞ for some nonsingular matrix H. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data observed on a grid, we propose… (More)

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