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February 2009 Asymptotic inference for semiparametric association models
Gerhard Osius
Ann. Statist. 37(1): 459-489 (February 2009). DOI: 10.1214/07-AOS572


Association models for a pair of random elements X and Y (e.g., vectors) are considered which specify the odds ratio function up to an unknown parameter θ. These models are shown to be semiparametric in the sense that they do not restrict the marginal distributions of X and Y. Inference for the odds ratio parameter θ may be obtained from sampling either Y conditionally on X or vice versa. Generalizing results from Prentice and Pyke, Weinberg and Wacholder and Scott and Wild, we show that asymptotic inference for θ under sampling conditional on Y is the same as if sampling had been conditional on X. Common regression models, for example, generalized linear models with canonical link or multivariate linear, respectively, logistic models, are association models where the regression parameter β is closely related to the odds ratio parameter θ. Hence inference for β may be drawn from samples conditional on Y using an association model.


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Gerhard Osius. "Asymptotic inference for semiparametric association models." Ann. Statist. 37 (1) 459 - 489, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62015
MathSciNet: MR2488359
Digital Object Identifier: 10.1214/07-AOS572

Primary: 62F12 , 62H05
Secondary: 62J05 , 62J12

Keywords: generalized linear model , I-projection , Log-bilinear association , logistic regression , multivariate linear regression , odds ratio , Semiparametric model

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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