## 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.

### 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

Zbl 0507.62026
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