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

Wei-Ying Wu, Chae Young Lim and Yimin Xiao

Journal of Multivariate Analysis, 2013, vol. 116, issue C, 74-91

Abstract: Consider a stationary Gaussian random field on Rd 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 objective function, which can be viewed as a weighted local Whittle likelihood, study their properties under the fixed-domain asymptotics and provide simulation results.

Keywords: Fixed-domain asymptotics; Fractal index; Fractal dimension; Gaussian random fields; Infill asymptotics; Microergodic parameter; Whittle likelihood (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2012.11.014

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