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

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.


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


Zbl 0507.62026
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