Orthogeodesic models
type: Item
instance of: scholarly article
title: Orthogeodesic models
zbMATH Open document ID: 0815.62005
author: Ole E. Barndorff-Nielsen
author: Preben Blæsild
published in: The Annals of Statistics
publication date: 1995-06-29T00:00:00Z
review text: Some composite transformation models have properties similar to certain of the properties of exponential models with affine dual foliations. The properties in question are of a geometrical nature. The present paper represents an attempt to give a unified delineation of those properties, in differential geometric terms. More specifically, we define, by purely differential geometric conditions, a class of parametric statistical models which we call orthogeodesic models and which comprises the exponential models with affine dual foliations as well as the composite transformation models that we had noted for their similarity with such exponential models. Except for general smoothness assumptions, we use five conditions to define an orthogeodesic model. These are stated in Section 3, which also contains a number of examples. Section 4 consists of a discussion of the implications of the four defining conditions; in particular, it contains a result on higher-order asymptotic independence. In Section 5 we study what further properties can be inferred if the model is assumed to be exponential. Section 2 reviews some basic concepts from statistical differential geometry and establishes the notation used throughout the paper.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62F99
Mathematics Subject Classification ID: 53B99
zbMATH DE Number: 444793
zbMATH Keywords: affine connections
zbMATH Keywords: alpha-connections
zbMATH Keywords: expected information
zbMATH Keywords: flat submanifolds
zbMATH Keywords: geodesic submanifolds
zbMATH Keywords: location-scale models
zbMATH Keywords: parallel submanifolds
zbMATH Keywords: pivot
zbMATH Keywords: proper dispersion models
zbMATH Keywords: statistical differential geometry
zbMATH Keywords: Student distribution
zbMATH Keywords: parallel models
zbMATH Keywords: composite transformation models
zbMATH Keywords: exponential models
zbMATH Keywords: affine dual foliations
zbMATH Keywords: orthogeodesic models
zbMATH Keywords: higher-order asymptotic independence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349162
OpenAlex ID: W4256561773
DOI: 10.1214/AOS/1176349162
description: scientific article; zbMATH DE number 444793