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Title: Whittle likelihood for irregularly spaced spatial data Authors:  Soutir Bandyopadhyay - Colorado School of Mines (United States) [presenting]
Abstract: Under some regularity conditions, including that the process is Gaussian, the sampling region is rectangular, and that the parameter space $\Theta$ is compact, it has been shown that the Whittle estimator $\widehat{\theta}_{n}$ minimizing their version of Whittle likelihood is consistent (for $d\leq 3$). One can construct large sample confidence regions for covariance parameters $\theta$ using the asymptotic normality of the Whittle estimator $\widehat{\theta}_{n}$. However, this requires to estimate the asymptotic covariance matrix, which involves integrals of the spatial sampling density. Moreover, nonparametric estimation of the quantities in the asymptotic covariance matrix requires specification of a smoothing parameter and is subject to the curse of dimensionality. In comparison, we propose a spatial frequency domain empirical likelihood-based approach which can be employed to produce asymptotically valid confidence regions and tests on $\theta$, without requiring explicit estimation of such quantities.