The Role of Differential Geometry in Statistical Theory
There has been increasing emphasis recently on the use of differential geometry in statistical theory, especially in asymptotic theory. In this paper a brief relatively nontechnical account is given of some relevant ideas in differential geometry. Some of the early work applying differential geometr...
| Veröffentlicht in: | International Statistical Review / Revue Internationale de Statistique. - Blackwell Publishing Ltd. - 54(1986), 1, Seite 83-96 |
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| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1986
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| Zugriff auf das übergeordnete Werk: | International Statistical Review / Revue Internationale de Statistique |
| Schlagworte: | Affine connection Asymptotic theory Curvature Curved exponential family Distance between distributions Expected and observed information Nonlinear regression Riemannian space Tensors Mathematics |
| Zusammenfassung: | There has been increasing emphasis recently on the use of differential geometry in statistical theory, especially in asymptotic theory. In this paper a brief relatively nontechnical account is given of some relevant ideas in differential geometry. Some of the early work applying differential geometry in statistics is then sketched. Recent developments are outlined and finally directions of current and possible future work are indicated. /// Récemment on a appuyé sur l'usage de géometrie différentielle en théorie statistique, particulièrement en théorie asymptotique. Dans cet article on décrit, relativement court et non-technique, quelques idées de la géométrie différentielle qui ont rapport à la statistique. Une partie du travail antérieur est ensuite esquissée. Le contour des développements récents est dessiné et enfin les directions du travail courant et éventuel à l'avenir sont indiquées. |
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| ISSN: | 17515823 |
| DOI: | 10.2307/1403260 |