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Abstract Details

Activity Number: 188
Type: Contributed
Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #308667
Title: Probabilistic Index Models: Semiparametric Regression Models for P(Y < Y*)
Author(s): Jan De Neve*+ and Olivier Thas and Lieven Clement and Jean-Pierre Ottoy
Companies: Ghent University and Ghent University and Ghent University and Ghent University
Address: , Ghent, International, 9000, Belgium
Keywords: semiparametric inference ; Wilcoxon-Mann-Whitney test ; probabilistic index ; AUC regression ; regression models ; rank statistics

We present a semiparametric statistical model for the probabilistic index which is defined as P(Y < Y*), where Y and Y* are independent random response variables associated with covariate patterns X and X*, respectively. In particular, we consider the model P(Y < Y*) = m(X,X*), where m(.,.) defines the relation between the probabilistic index and the predictors. Asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory. The framework includes the Wilcoxon rank sum test and the Kruskal-Wallis test corrected for covariates. Our work is related to, but extends the methods of Brumback et al. Statist. Med. 2006; 25:575-590. The model is illustrated on several examples, and the estimation theory is validated in a simulation study.

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