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.


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