Abstract:
The consistency problem is investigated for estimates of the conditional expectation types for random variables with a countable set of values according to observations of random processes in discrete time. Necessary and sufficient conditions for strong consistency are obtained in terms of the characteristics of the likelihood ratio of certain special probability measures. It is shown that the more detailed characterization of observed random processes makes it possible to obtain the consistency condition in terms of their probability characteristics. Consistency conditions are given for parameter estimates obtained from observations of the paths of a Markov chain and a Gaussian process.
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