ASYMPTOTIC INFERENCE FOR SEMIPARAMETRIC ASSOCIATION MODELS

• 成果类型: Article
• 署名作者: Osius, Gerhard
• 署名单位: University of Bremen; Leibniz Association; Leibniz Institute for Prevention Research & Epidemiology (BIPS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS572
• 发表日期: 2009
• 页码: 459-489
• 关键词: contingency-tables; regression

摘要

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 theta. 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 theta 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 theta under sampling conditional oil 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 beta is closely related to the odds ratio parameter theta. Hence inference for beta may be drawn from samples conditional oil Y using an association model.