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Probabilistic index models
Address for correspondence: Olivier Thas, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure Links 653, B‐9000 Gent, Belgium. E‐mail: Olivier.Thas@UGent.be
Abstract
Summary. We present a semiparametric statistical model for the probabilistic index which can be defined as P(YY*), where Y and Y* are independent random response variables associated with covariate patterns X and X* respectively. A link function defines the relationship between the probabilistic index and a linear predictor. Asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory. The model is illustrated with several examples, and the estimation theory is validated in a simulation study.
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