Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 74, Issue 4, Pages 623-671Publisher
OXFORD UNIV PRESS
DOI: 10.1111/j.1467-9868.2011.01020.x
Keywords
Area under the curve regression; Semiparametric inference; Stress-strength; Wilcoxon-Mann-Whitney test
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Funding
- Interuniversity Attraction Pole research network grant of the Belgian Government (Belgian science policy) [P6/03]
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We present a semiparametric statistical model for the probabilistic index which can be defined as P(Y <= Y*), 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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