ON ASYMPTOTICALLY OPTIMAL ESTIMATES FOR GENERAL OBSERVATIONS

Asymptotically maximum likelihood estimators and estimators asymptotic ally minimizing criterial functions of observations are considered in statistical models with generalized sequences of observations. New nec essary and sufficient conditions for consistency of these estimators a re established. The applicability of these conditions is illustrated o n regression models with Gaussian and contaminated observations and on models of exponentially distributed random processes and fields. (C) 1997 Elsevier Science B.V.