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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Blasphemy

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.

incision

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