Titlebook: Asymptotic Expansions for General Statistical Models; Johann Pfanzagl Book 1985 Springer-Verlag Berlin Heidelberg 1985 approximation.behav

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Joachim W. Schmidt,Constantino Thanose quality of such confidence procedures, defined in terms of covering probabilities, can be equivalently expressed by the concentration of the confidence bound. Results on the concentration of confidence bounds can be applied in particular to the concentration of estimators.

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Fusing Content and Context with Causality,the concentration of estimators). The question whether these bounds are attainable, and how procedures attaining these bounds can be obtained, was partially answered by results of the type “1st order efficiency implies 2nd order efficiency” (see Proposition 6.4.4 and Theorem 8.7.1). In the present c

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https://doi.org/10.1007/978-1-4842-0749-9β→ℝ. by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds.

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Introduction,β→ℝ. by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds.

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Asymptotic Expansions for Power Functions,tic log(.) are most powerful for . against .. In this section it will be shown that sequences of test statistics log(.), n ∈ ℕ, are most powerful of order o(n.) under relatively weak conditions on the remainder sequence R., n ∈ ℕ.

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Evaluating the Performance of Estimators,luate the concentration of its distribution, P*K, about κ(P). In the following sections we provide the conceptual framework for this task. In Section 7.2 we introduce the concept of a randomized estimator.