Tail estimation of the spectral density for a stationary Gaussian random field

Consider a stationary Gaussian random field on R^d with spectral density f(@l) that satisfies f(@l)~c|@l|^-^@q as |@l|->~. The parameters c and @q control the tail behavior of the spectral density. c is related to a microergodic parameter and @q is related to a fractal index. For data observed on a grid, we propose estimators of c and @q by minimizing an objective function, which can be viewed as a weighted local Whittle likelihood, study their properties under the fixed-domain asymptotics and provide simulation results.

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