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Abstract |
There are at least two different asymptotic frameworks in spatial statistics depending whether the spatial domain is bounded or not: The increasing domain asymptotic framework where the spatial domain increases, and the fixed-domain or infill asymptotic framework where the spatial domain is bounded. Asymptotic results are quite different under the two asymptotic framework. For example, for some well-known covariance functions, the variance and the range parameter are not consistently estimable under the infill asymptotic framework---that is, consistent estimators do not exist. However, they are both consistently estimable and the maximum likelihood estimators are asymptotically normal under mild regularity conditions under the increasing domain asymptotic framework. I will provide some guideline as to which asymptotic framework should be used for a given spatial data set, and discuss some applications of the infill asymptotics to the analysis of massive spatial data. |
