Summary
Let X 0, X 1,⋯, X nbe r.v.'s coming from a stochastic process whose finite dimensional distributions are of known functional form except that they involve a k-dimensional parameter. From the viewpoint of statistical inference, it is of interest to obtain the asymptotic distributions of the log-likelihood function and also of certain other r.v.'s closely associated with the likelihood function. The probability measures employed for this purpose depend, in general, on the sample size n. These problems are resolved provided the process satisfies some quite general regularity conditions. The results presented herein generalize previously obtained results for the case of Markovian processes, and also for i.n.n.i.d. r.v.'s. The concept of contiguity plays a key role in the various derivations.
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This research was supported by the National Science Foundation, Grant MCS76-11620, and a grant by the National Research Foundation of Greece
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Roussas, G.G. Asymptotic distribution of the log-likelihood function for stochastic processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 47, 31–46 (1979). https://doi.org/10.1007/BF00533249
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DOI: https://doi.org/10.1007/BF00533249