###
MAXIMUM LIKELIHOOD ESTIMATION IN EXPONENTIAL

ORTHOGEODESIC MODELS

###
PREBEN BLÆ SILD

*Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus,*

Ny Munkegade, DK-8000, Aarhus C, Denmark
(Received September 1, 1992; revised May 24, 1993)

**Abstract.**
An orthogeodesic statistical model is
defined in terms of five conditions of differential geometric
nature. These conditions are reviewed together with a
characterization theorem for exponential orthogeodesic models.
Orthogonal projections, relevant for maximum likelihood
estimation in exponential orthogeodesic models, are described
in a simple way in terms of some of the quantities in the
characterization theorem. A unified procedure for performing
maximum likelihood estimation in exponential orthogeodesic models
is given and the use of this procedure is illustrated for some
of the most important models of this kind such as
*theta*-parallel models, *tau*-parallel models and certain
transformation models.

*Key words and phrases*:
Affine *alpha*-connections,
expected information, flat submanifolds, geodesic submanifolds,
likelihood equations, orthogonal projections, pivot,
transformation models, *tau*-parallel models, *theta*-parallel
models.

**Source**
( TeX ,
DVI ,
PS )