## The Annals of Statistics

### Confidence Regions in Curved Exponential Families: Application to Matched Case-Control and Survival Studies with General Relative Risk Function

#### Abstract

Differential geometric methods are used to construct approximate confidence regions for curved exponential families. The $\alpha$-connection geometries discussed by Amari (1982), 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.

#### Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 346-359.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350270

Digital Object Identifier
doi:10.1214/aos/1176350270

Mathematical Reviews number (MathSciNet)
MR885741

Zentralblatt MATH identifier
0646.62026

JSTOR