Inference for Stationary Random Fields given Poisson Samples.
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MATHEMATICS
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This paper examines some questions of statistical inference -- specifically, estimation of the mean and covariance function, as well as linear state estimation -- for stationary random fields observable only at the points of a likewise Poisson process. Given a d-dimensional random field and a Poisson process independent of it, suppose that it is possible to observe only the location of each point of the Poisson process and the value of the random field at that randomly located point. Nonparametric estimators of the mean and covariance function of the random field - based on observation over compact sets of single realizations of the Poisson samples - are constructed. Under fairly mild conditions these estimators are consistent in various senses as the set of observation becomes unbounded in a suitable manner. The state estimation problem of minimum mean squares reconstruction of unobserved values of the random field is also examined.
- Statistics and Probability