MAXIMUM-LIKELIHOOD-ESTIMATION IN EXPONENTIAL ORTHOGEODESIC MODELS

An orthogeodesic statistical model is defined in terms of five conditi ons of differential geometric nature. These conditions are reviewed to gether with a characterization theorem for exponential orthogeodesic m odels. Orthogonal projections, relevant for maximum likelihood estimat ion 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 exp onential orthogeodesic models is given and the use of this procedure i s illustrated for some of the most important models of this kind such as theta-parallel models, tau-parallel models and certain transformati on models.