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Probabilistic index models
Author(s) -
Thas Olivier,
Neve Jan De,
Clement Lieven,
Ottoy JeanPierre
Publication year - 2012
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2011.01020.x
Subject(s) - estimator , mathematics , asymptotic distribution , probabilistic logic , covariate , statistics , covariance , consistency (knowledge bases) , index (typography) , statistical model , statistical inference , normality , econometrics , computer science , discrete mathematics , world wide web
Summary. 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.