Confidence regions in curved exponential families: Application to matched case-control and survival studies with general relative risk function. (English) Zbl 0646.62026

Moolgavkar, Suresh H.; Venzon, David J.

Ann. Stat. 15, 346-359 (1987).

Summary: Differential geometric methods are used to construct approximate confidence regions for curved exponential families. The \(\alpha\)- connection geometries discussed by S. I. Amari [Ann. Stat. 10, 357- 385 (1982; Zbl 0507.62026)], and another geometry introduced here, the c- geometry, are exploited to construct confidence regions. Survival and case-control studies with general relative risk functions are interpreted in the context of curved exponential families, and an example illustrates the construction of confidence regions for matched case-control studies. Simulations indicate that the geometric procedures have good coverage and power properties.

MSC:

62F25	Parametric tolerance and confidence regions
62E20	Asymptotic distribution theory in statistics
62B10	Statistical aspects of information-theoretic topics
53B05	Linear and affine connections
53B21	Methods of local Riemannian geometry
62F12	Asymptotic properties of parametric estimators

Keywords:

geodesic coordinates; logistic regression; partial likelihood; Fisher information matrix; alpha connections; variance-stabilizing parametrizations; Wald regions; approximate confidence regions; curved exponential families; c-geometry; Survival; general relative risk functions; matched case-control studies; Simulations; coverage and power properties

Citations:

Zbl 0507.62026