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Abstract:
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Gaussian likelihood inference has been studied and used extensively both in theory and applications due to its simplicity. However, to analyze spatial data, the assumption of Gaussianity is rarely met in practice. In this work we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By means of Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field with Matérn covariance function, where g is a parameter controlling skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity on the estimated covariance function by means of functional boxplots. We also provide theoretical asymptotic results to characterize these effects for an exponential covariance function.
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