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September, 1991 A Geometric Approach to Detecting Influential Cases
Paul W. Vos
Ann. Statist. 19(3): 1570-1581 (September, 1991). DOI: 10.1214/aos/1176348262


Amari's dual geometries are used to study measures of influence in exponential family regression. The dual geometries are presented as a natural extension of the Euclidean geometry used for the normal regression model. These geometries are then used to extend Cook's distance to generalized linear models and exponential family regression. Some of these extensions lead to measures already considered while other extensions lead to new measures of influence. The advantages of one of these new measures are discussed.


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Paul W. Vos. "A Geometric Approach to Detecting Influential Cases." Ann. Statist. 19 (3) 1570 - 1581, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62067
MathSciNet: MR1126338
Digital Object Identifier: 10.1214/aos/1176348262

Primary: 62J02
Secondary: 62F99

Keywords: Dual geometries , exponential families , generalized linear models , influence measures , Kullback divergence , parameter invariance

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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