| Abstract: | 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. |
