Predicting random fields with increasing dense observations. (English) Zbl 0955.62095

Stein, Michael L.

Ann. Appl. Probab. 9, No. 1, 242-273 (1999).

This paper deals with the spectral characteristics of the errors of optimal linear predictors for weakly stationary random fields. The work gives a number of new rates of convergence to optimality for predictors based on an incorrect spectral density when the ratio of the incorrect to the correct spectral density tends to 1 at high frequencies.

Reviewer: Pedro A.Morettin (São Paulo)

MSC:

62M20	Inference from stochastic processes and prediction
62M40	Random fields; image analysis
41A25	Rate of convergence, degree of approximation

Keywords:

approximations in Hilbert spaces; time series experiments; infill asymptotics; kriging; sampling theorem

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