Conditions for Consistency of MLE’s
Igor Vajda · Contributions to statistics · 1994
It is proved that the MLE of a deterministic signal in i. i. d. noise may be inconsistent when the noise distribution has a heavy tail. A simplified version of the necessary and sufficient condition for consistency of MLE’s found in Vajda (1993) is formulated for models with i. i. d. observations and with parameters from reasonable metric spaces. It is shown that this condition implies the consistency of all “approximate MLE’s“ and its contrary implies the inconsistency of all these estimators. Further, a statistical uncertainty of parametric sets is introduced and the mentioned condition is reformulated in terms of this uncertainty.