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ON CONFIDENCE REGIONS OF EMBEDDED MODELS IN REGULAR PARAMETRIC FAMILIES (A GEOMETRIC APPROACH)
Author(s) -
Wei BoCheng
Publication year - 1994
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1994.tb00885.x
Subject(s) - parametric statistics , mathematics , extension (predicate logic) , parametric equation , parametric model , confidence interval , nonlinear system , nonlinear regression , geometric modeling , algorithm , computer science , regression analysis , statistics , geometry , physics , quantum mechanics , programming language
Summary Regular parametric families are commonly encountered in statistical problems (e.g. Cox & Hinkley, 1974). In this paper, we propose a differential geometric framework for the embedded models in these families. Our framework may be regarded as an extension of that presented by Bates & Watts (1980) for nonlinear regression models. As an application, we use this geometric framework to derive three kinds of improved approximate confidence regions for the parameter and parameter subsets in terms of curvatures. The results obtained by Hamilton et al. (1982) and Hamilton (1986) are extended to embedded models in regular parametric families.