Asymptotic Expansions for General Statistical Models

Johann Pfanzagl (Autor)

Buch | Softcover

509 Seiten

1985
Springer-Verlag New York Inc.
9780387962214 (ISBN)

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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.

Reihe/Serie	Lecture Notes in Statistics ; 31
Mitarbeit	Assistent: W. Wefelmeyer
Zusatzinfo	1 Illustrations, black and white; VII, 509 p. 1 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	170 x 244 mm
Gewicht	887 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Statistik
ISBN-13	9780387962214 / 9780387962214
Zustand	Neuware