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

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发表于 2025-3-21 20:09:29 | 显示全部楼层 |阅读模式
期刊全称Asymptotic Expansions for General Statistical Models
影响因子2023Johann Pfanzagl
视频video
学科分类Lecture Notes in Statistics
图书封面Titlebook: Asymptotic Expansions for General Statistical Models;  Johann Pfanzagl Book 1985 Springer-Verlag Berlin Heidelberg 1985 approximation.behav
影响因子0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k 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. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its con
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A Logic-Based Calculus of Eventsluate 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.
发表于 2025-3-22 05:26:45 | 显示全部楼层
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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Lecture Notes in Statisticshttp://image.papertrans.cn/b/image/163801.jpg
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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.
发表于 2025-3-22 20:46:46 | 显示全部楼层
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.
发表于 2025-3-23 01:01:54 | 显示全部楼层
Asymptotic Bounds for the Performance of Confidence Procedures and Estimators,e 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.
发表于 2025-3-23 01:49:26 | 显示全部楼层
https://doi.org/10.1007/978-3-319-97943-4Let β be a family of mutually absolutely continuous p-measures. We fix a dominating measure μ, and use the small letter p to denote the μ-density of P ∈ β.
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https://doi.org/10.1007/978-3-319-97943-4The concept of a differentiable path is motivated by the aspiration to describe the local structure of a given family of p-measures. Our purpose is to grasp those local properties which are relevant for the asymptotic performance of statistical procedures.
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