Abstract. The paper examines the properties of consistency and asymptotic normality of maximum likelihood estimate for Markov sequences with Gibbs distribution. Theorems that allow approximating the criterion function of the Markov process with a single point of minimum by its empirical estimate are formulated and proved. The results can be applied to analyze the convergence of unknown parameters to their true values.
Keywords: Gibbs distribution, maximum likelihood method, Markov random field, stochastic process, parameter estimation.
Самосёнок Александр Сергеевич,
младший научный сотрудник Института кибернетики им. В.М. Глушкова НАН Украины, Киев,
e-mail: samosyonok@gmail.com.