The Annals of Statistics

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

Suresh H. Moolgavkar and David J. Venzon

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62B10: Information-theoretic topics [See also 94A17]

Keywords
Alpha connections differential geometry inference logistic regression partial likelihood variance-stabilizing parametrizations

Citation

Moolgavkar, Suresh H.; Venzon, David J. Confidence Regions in Curved Exponential Families: Application to Matched Case-Control and Survival Studies with General Relative Risk Function. Ann. Statist. 15 (1987), no. 1, 346--359. doi:10.1214/aos/1176350270. https://projecteuclid.org/euclid.aos/1176350270


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