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Wald's (1949) classical consistency theorem (which proves strong consistency of the maximum likelihood estimator when the observations are independent and identically distributed) is extended to cover the case of dependent observations. Three consistency theorems for dependent observations are proved under conditions which, in our opinion, are weaker (and more readily applicable) than usual: (i) the regularity conditions do not involve derivatives of the likelihood function, (ii) no uniform convergence assumption is made, (iii) the parameter space need not be compact, (iv) the number of parameters, though fixed and finite, is arbitrary, and (v) the true distribution underlying the observations need not be specified.


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