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Applications of differential geometry to statistics

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Marriott, Paul (1990) Applications of differential geometry to statistics. PhD thesis, University of Warwick.

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Abstract

Chapters 1 and 2 are both surveys of the current work in applying
geometry to statistics. Chapter 1 is a broad outline of all the work done so far,
while Chapter 2 studies, in particular, the work of Amari and that of Lauritzen.
In Chapters 3 and 4 we study some open problems which have been raised
by Lauritzen's work. In particular we look in detail at some of the differential
geometric theory behind Lauritzen's defmition of a Statistical manifold.
The following chapters follow a different line of research. We look at a new
non symmetric differential geometric structure which we call a preferred point
manifold. We show how this structure encompasses the work of Amari and
Lauritzen, and how it points the way to many generalizations of their results. In
Chapter 5 we define this new structure, and compare it to the Statistical manifold
theory. Chapter 6 develops some examples of the new geometry in a statistical
context. Chapter 7 starts the development of the pure theory of these preferred
point manifolds.
In Chapter 8 we outline possible paths of research in which the new
geometry may be applied to statistical theory.
We include, in an appendix, a copy of a joint paper which looks at some
direct applications of differential geometry to a statistical problem, in this case it is
the problem of the behaviour of the Wald test with nonlinear restriction functions.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Mathematical statistics, Geometrical models in statistics, Amari, Shun’ichi, Lauritzen, Steffen L., Geometry, Differential
Official Date: May 1990
Dates:
DateEvent
May 1990Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Eells, James, 1926-2007
Sponsors: Science and Engineering Research Council (Great Britain) (SERC)
Extent: 1 volume, (various pagings)
Language: eng

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