Titlebook: Asymptotic Stochastics; An Introduction with Norbert Henze Textbook 20241st edition The Editor(s) (if applicable) and The Author(s), under

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Costume

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Maximum Likelihood Estimation,t main result is the strong consistency of ML estimators under weak conditions on the density, provided that the parameter space is a compact set. The second main result is the asymptotic normality of the ML estimator under standard regularity conditions on the density, provided that the sequence of ML estimators is consistent.

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Probability Measures on Metric Spaces, functions defined on the unit interval, equipped with the supremum distance. In this space, relative compact subsets are characterized by the Arzelà-Ascoli theorem. The sigma-field of Borel sets in C[0,1] is generated by the field of finite-dimensional sets. Further basic terms introduced in this chapter are ., and

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LOPE

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A Poisson Limit Theorem for Triangular Arrays,orem for the row totals of such an array, provided that this array is asymptotically negligible in a certain sense. This result, which is a far-reaching generalization of the law of rare events, is remarkable inasmuch it provides a condition for convergence in distribution to a Poisson distribution