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 orthogenodesic models is given and the use of this procedure is illustrated for some of the most important models of this kind such as ϑ-parallel models, τ-parallel models and certain transformation models.
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References
Barndorff-Nielsen, O. E. (1978).Information and Exponential Families in Statistical Theory, Wiley, Chichester.
Barndorff-Nielsen, O. E. (1988).Parametric Statistical Models and Likelihood, Springer, Heidelberg.
Barndorff-Nielsen, O. E. and Blæsild, P. (1983a). Exponential models with affine dual foliations,Ann. Statist.,11, 753–769.
Barndorff-Nielsen, O. E. and Blæsild, P. (1983b). Reproductive exponential families,Ann. Statist.,11, 770–782.
Barndorff-Nielsen, O. E. and Blæsild, P. (1993). Orthogeodesic models,Ann. Statist.,21, 1018–1039.
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Blæsild, P. Maximum likelihood estimation in exponential orthogeodesic models. Ann Inst Stat Math 46, 43–55 (1994). https://doi.org/10.1007/BF00773591
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DOI: https://doi.org/10.1007/BF00773591