ASYMPTOTIC INFERENCE FOR SEMIPARAMETRICASSOCIATION MODELS

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 para-meter θ. These models are shown to be semiparametric in the sense that theydo not restrict the marginal distributions of X and Y. Inference for the oddsratio parameter θ may be obtained from-sampling either Y conditionally on Xor vice versa. Generalizing results from Prentice and Pyke, Weinberg and Wa-cholder and Scott and Wild, we show that asymptotic inference for θ undersampling conditional on Y is the same as if sampling had been conditionalon X. Common regression models, for example, generalized linear modelswith canonical link or multivariate linear, respectively, logistic models, areassociation models where the regression parameter β is closely related to theodds ratio parameter θ. Hence inference for β may be drawn from samplesconditional on Y using an association model.