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Author : Johann Pfanzagl
Release : 1982
Genre : Mathematical statistics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Contributions to a General Asymptotic Statistical Theory by : Johann Pfanzagl
Download or read book Contributions to a General Asymptotic Statistical Theory written by Johann Pfanzagl. This book was released on 1982. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Pfanzagl
Release : 1982-11-01
Genre : Mathematics
Kind : eBook
Book Rating : 765/5 ( reviews)
Book Synopsis Contributions to a General Asymptotic Statistical Theory by : J. Pfanzagl
Download or read book Contributions to a General Asymptotic Statistical Theory written by J. Pfanzagl. This book was released on 1982-11-01. Available in PDF, EPUB and Kindle. Book excerpt: The aso theory developed in Chapters 8 - 12 presumes that the tan gent cones are linear spaces. In the present chapter we collect a few natural examples where the tangent cone fails to be a linear space. These examples are to remind the reader that an extension of the theo ry to convex tangent cones is wanted. Since the results are not needed in the rest of the book, we are more generous ab out regularity condi tions. The common feature of the examples is the following: Given a pre order (i.e., a reflexive and transitive order relation) on a family of p-measures, and a subfamily i of order equivalent p-measures, the fa mily ~ consists of p-measures comparable with the elements of i. This usually leads to a (convex) tangent cone 1f only p-measures larger (or smaller) than those in i are considered, or to a tangent co ne con sisting of a convex cone and its reflexion about 0 if both smaller and larger p-measures are allowed. For partial orders (i.e., antisymmetric pre-orders), ireduces to a single p-measure. we do not assume the p-measures in ~ to be pairwise comparable.
Author : J. Pfanzagl
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 697/5 ( reviews)
Book Synopsis Contributions to a General Asymptotic Statistical Theory by : J. Pfanzagl
Download or read book Contributions to a General Asymptotic Statistical Theory written by J. Pfanzagl. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Johann Pfanzagl
Release : 2013-11-27
Genre : Mathematics
Kind : eBook
Book Rating : 794/5 ( reviews)
Book Synopsis Asymptotic Expansions for General Statistical Models by : Johann Pfanzagl
Download or read book Asymptotic Expansions for General Statistical Models written by Johann Pfanzagl. This book was released on 2013-11-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Kuang-Fu Cheng
Release : 1979
Genre : Characteristic functions
Kind : eBook
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Book Synopsis Contributions to Asymptotic Theory for Statistics as Functionals of the Empirical Density Function by : Kuang-Fu Cheng
Download or read book Contributions to Asymptotic Theory for Statistics as Functionals of the Empirical Density Function written by Kuang-Fu Cheng. This book was released on 1979. Available in PDF, EPUB and Kindle. Book excerpt:
