Consistency of Maximum Likelihood Estimators for Multiparameter Markov Chains

Abstract

Abstract Billingsley’s [2] proof of the consistency theorem for the multiparameter discrete state space Markov chains includes the assumptions of existence and continuity of all third partial derivatives. In this paper, we relaxed the assumptions to include the existence and continuity of the derivatives only up to the second order. Also, we establish conditions implying the assumptions of the main theorem with the requirement of the boundedness and not the continuity of the third order derivatives.