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Probabilistic index models

Olivier Thas (UGent) , Jan De Neve (UGent) , Lieven Clement (UGent) and Jean-Pierre Ottoy (UGent)
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Abstract
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.
Keywords
GENERALIZED LINEAR-MODELS, REGRESSION-MODELS, LONGITUDINAL DATA-ANALYSIS, INTUITIVE NONPARAMETRIC APPROACH, Wilcoxon-Mann-Whitney test, Stress-strength, Area under the curve regression, Semiparametric inference, KRUSKAL-WALLIS, MARGINAL MODELS, LISTENING TESTS, MOMENT RESTRICTIONS, ROC CURVE, CLINICAL-TRIALS

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MLA
Thas, Olivier, Jan De Neve, Lieven Clement, et al. “Probabilistic Index Models.” JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 74.4 (2012): 623–671. Print.
APA
Thas, O., De Neve, J., Clement, L., & Ottoy, J.-P. (2012). Probabilistic index models. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 74(4), 623–671.
Chicago author-date
Thas, Olivier, Jan De Neve, Lieven Clement, and Jean-Pierre Ottoy. 2012. “Probabilistic Index Models.” Journal of the Royal Statistical Society Series B-statistical Methodology 74 (4): 623–671.
Chicago author-date (all authors)
Thas, Olivier, Jan De Neve, Lieven Clement, and Jean-Pierre Ottoy. 2012. “Probabilistic Index Models.” Journal of the Royal Statistical Society Series B-statistical Methodology 74 (4): 623–671.
Vancouver
1.
Thas O, De Neve J, Clement L, Ottoy J-P. Probabilistic index models. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY. 2012;74(4):623–71.
IEEE
[1]
O. Thas, J. De Neve, L. Clement, and J.-P. Ottoy, “Probabilistic index models,” JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, vol. 74, no. 4, pp. 623–671, 2012.
@article{1934532,
  abstract     = {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.},
  author       = {Thas, Olivier and De Neve, Jan and Clement, Lieven and Ottoy, Jean-Pierre},
  issn         = {1467-9868},
  journal      = {JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY},
  keywords     = {GENERALIZED LINEAR-MODELS,REGRESSION-MODELS,LONGITUDINAL DATA-ANALYSIS,INTUITIVE NONPARAMETRIC APPROACH,Wilcoxon-Mann-Whitney test,Stress-strength,Area under the curve regression,Semiparametric inference,KRUSKAL-WALLIS,MARGINAL MODELS,LISTENING TESTS,MOMENT RESTRICTIONS,ROC CURVE,CLINICAL-TRIALS},
  language     = {eng},
  number       = {4},
  pages        = {623--671},
  title        = {Probabilistic index models},
  url          = {http://dx.doi.org/10.1111/j.1467-9868.2011.01020.x},
  volume       = {74},
  year         = {2012},
}

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