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Probabilistic index models. With discussion and authors’ reply. (English) Zbl 1411.62120

Summary: We present a semiparametric statistical model for the probabilistic index which can be defined as \(P(Y\leqslant Y^\ast)\), where \(Y\) and \(Y^\ast\) are independent random response variables associated with covariate patterns \(\mathbf{X}\) and \(\mathbf{X}^\ast\) 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.

MSC:

62G20 Asymptotic properties of nonparametric inference
62G10 Nonparametric hypothesis testing
62G05 Nonparametric estimation
62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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