On non-consistency of estimators
Yury A. Kutoyants, L. JU. Vostrikova · Stochastics and stochastics reports · 1995
Let be a sequence of general filtered statistical parametric models. We describe the limit behaviour of the maximum likelihood estimators and of the Bayesian estimators of θ when the necessary conditions of existence of a consistent estimator of θ are not satisfied. As examples we consider statistical models corresponding to a sequence of independent random variables, Poisson processes, diffusion processes.