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Hellinger distance estimation of strongly dependent Gaussian random fields. (English. French summary) Zbl 1412.60056

Summary: The Minimum Hellinger Distance Estimator (MHDE) of density function is investigated for stationary long memory (long-range dependent) random fields observed over a finite set of spatial points. A general result on the consistency of the MHD Estimator is first obtained and then, under some mild assumptions, the asymptotic distribution of this estimator is established.

MSC:

60G10 Stationary stochastic processes
60G15 Gaussian processes
60G60 Random fields
62F12 Asymptotic properties of parametric estimators
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Full Text: Euclid