Asymptotic Expansions for General Statistical Models - Lecture Notes in Statistics - Johann Pfanzagl - Books - Springer-Verlag New York Inc. - 9780387962214 - October 25, 1985
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Johann Pfanzagl
Asymptotic Expansions for General Statistical Models - Lecture Notes in Statistics 1985 edition

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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 concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.

516 pages, 1 black & white illustrations, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released October 25, 1985
ISBN13 9780387962214
Publishers Springer-Verlag New York Inc.
Pages 516
Dimensions 170 × 244 × 27 mm   ·   887 g
Language English  
Contributor W. Wefelmeyer

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