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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A Central Limit Theorem for Stationary ,-Dependent Sequences,nce . of random variables means that, for each . and ., the distribution of the random vector . does not depend on . and thus is invariant to time shifts. In particular, all the . have the same distribution. Moreover, we assume that, for some non-negative integer ., this sequence is .-dependent, whi

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The Multivariate Normal Distribution,variate normal distribution. A .-dimensional random vector . is said to have a .-variate normal distribution if each linear combination of its components has a (possibly degenerate) univariate normal distribution. This definition immediately entails that any collection of components of . has a (lowe

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Maximum Likelihood Estimation,od of maximum likelihood (ML). This method, which has a long history, is applicable if the random variables on which the estimation is based have a density with respect to some dominating measure. The basic idea of ML estimation is to regard the parameter value that maximizes the joint density as a

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Asymptotic (Relative) Efficiency of Estimators,formation inequality of Fréchet-Cramér-Rao that, under certain regularity conditions, provides a lower bound for the variance of an estimator. After pointing out the bias-variance-tradeoff in connection with minimizing the mean squared estimation error, a proof of the multivariate information inequa

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Likelihood Ratio Tests,tio tests. As with the method of maximum likelihood, these tests presuppose densities with respect to some sigma-finite dominating measure. The chapter starts with compiling basic notions, such as .. These concepts are illustrated with the one-sided binomial test. Then, the Neyman-Person likelihood