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{1176350270,
author = {Moolgavkar, Suresh H. and Venzon, David J.},
title = {Confidence Regions in Curved Exponential Families: Application to Matched Case-Control and Survival Studies with General Relative Risk Function},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 346-359},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350270}
}
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., Tome 15 (1987) no. 1, pp. 346-359. http://gdmltest.u-ga.fr/item/1176350270/