Hellinger distance estimation of strongly dependent Gaussian random fields

Abstract

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.

Keywords: Asymptotic properties ; Strongly dependence ; Hellinger distance estimation, random field.

AMS 2010 Mathematics Subject Classification Objects : 60G10, 60G15, 60G60, 62F12