Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations
Copyright policy )Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncatedlikelihood functions. Truncated-likelihood functions are based on direct functional approximations of the presumed family of covariance functions. For compactly supported covariance functions, within an increasing-domain asymptotic framework, we provide sufficient conditions under which consistency and asymptotic normality of estimators based on truncated-likelihood functions are preserved. We apply our result to the family of generalized Wendland covariance functions and discuss several examples of Wendland approximations. For families of covariance functions that are not compactly supported, we combine our results with the covariance tapering approach and show that ML estimators, based on truncated-tapered likelihood functions, asymptotically minimize the Kullback-Leibler divergence, when the taper range is fixed.
- National Academy of Sciences of Ukraine Ukraine
- University of Zurich Switzerland
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
- Institute of Mathematics Czech Republic
secondary 41A99. Keywords and phrases: Gaussian random fields, Statistics and Probability, Inference from spatial processes, asymptotic normality, Mathematics - Statistics Theory, Probability and Uncertainty 60G15 - Gaussian processes 41 - Approximations and expansions 62F12 - Asymptotic properties of parametric estimators 62M40 - Random fields; image analysis Primary 60G15, Statistics Theory (math.ST), image analysis Primary 60G15, Non-Markovian processes: estimation, 62F12; secondary 41A99. Keywords and phrases: Gaussian random fields, 10231 Department of Astrophysics, Approximation by other special function classes, covariance tapering., 10127 Institute of Evolutionary Biology and Environmental Studies, covariance tapering, 510 Mathematics, FOS: Mathematics, 1804 Statistics, Probability and Uncertainty, 2613 Statistics and Probability, Asymptotic properties of parametric estimators, compactly supported covariance functions, Approximations and expansions 62F12, consistency, Probability and Uncertainty 60G15, Statistics, Asymptotic properties of parametric estimators 62M40, Gaussian random fields, likelihood approximations, 60G15, 62F12 (Primary) 41A99 (Secondary), 10123 Institute of Mathematics, Random fields, 62F12, Gaussian processes 41
secondary 41A99. Keywords and phrases: Gaussian random fields, Statistics and Probability, Inference from spatial processes, asymptotic normality, Mathematics - Statistics Theory, Probability and Uncertainty 60G15 - Gaussian processes 41 - Approximations and expansions 62F12 - Asymptotic properties of parametric estimators 62M40 - Random fields; image analysis Primary 60G15, Statistics Theory (math.ST), image analysis Primary 60G15, Non-Markovian processes: estimation, 62F12; secondary 41A99. Keywords and phrases: Gaussian random fields, 10231 Department of Astrophysics, Approximation by other special function classes, covariance tapering., 10127 Institute of Evolutionary Biology and Environmental Studies, covariance tapering, 510 Mathematics, FOS: Mathematics, 1804 Statistics, Probability and Uncertainty, 2613 Statistics and Probability, Asymptotic properties of parametric estimators, compactly supported covariance functions, Approximations and expansions 62F12, consistency, Probability and Uncertainty 60G15, Statistics, Asymptotic properties of parametric estimators 62M40, Gaussian random fields, likelihood approximations, 60G15, 62F12 (Primary) 41A99 (Secondary), 10123 Institute of Mathematics, Random fields, 62F12, Gaussian processes 41
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