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:	Date Event May 1990 Submitted
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Publication Status:	Unpublished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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