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Titlebook: Asymptotic Optimal Inference for Non-ergodic Models; Ishwar V. Basawa,David John Scott Book 1983 Springer-Verlag New York Inc. 1983 Branch

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Optimal Asymptotic Tests,nditions are required. It turns out that the usual statistics such as the Rao’s score statistic, the Neyman statistic, and the likelihood-ratio (LR) statistic exhibit non-standard asymptotic behaviour in the non-ergodic case, as regards efficiency and limit distributions.
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https://doi.org/10.1007/978-1-4612-5505-5Branching process; Estimator; Likelihood; Random variable; diffusion process; statistics
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978-0-387-90810-6Springer-Verlag New York Inc. 1983
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https://doi.org/10.1007/978-3-319-51777-3This chapter is concerned with the formulation of a model which generalises the classical Fisher-Rao-Le Cam model as previewed in Chapter 0, and a discussion of an asymptotic model which approximates the proposed general model.
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Classical physics on a finite phase spaceich attains the maximal possible concentration about the true value of the parameter. It is easy to show that such an estimator also has minimum mean square error, so the theory incorporates the classical notions of estimation efficiency. Of course it is not in general possible to obtain an estimato
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