Probabilistic index models
By Olivier Thas, J. D. Neve, Lieven Clement, J. Ottoy. 2012
177 citations recorded by the source corpus.
Summary. 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.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/9d913d5f9bb442c0bc8f086149a39b0d56ac743e
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Citations in the corpus
- Measurement: A Very Short Introduction—Rejoinder to discussion (2016, background): “For an example of recent developments in just one particular direction, see Thas (2012).”
- Most Likely Transformations (2015, methodology): “2013), probabilistic forecasting (Gneiting and Katzfuss 2014), distribution and quantile regression (Leorato and Peracchi 2015; Rothe and Wied 2013), probabilistic index models (Thas et al. 2012) and conditional transformation models (Hothorn et al.”
- Simple ways to interpret effects in modeling ordinal categorical data (2018, methodology): “Wenext present an alternativeway to summarize the effect of a categorical explanatory variable on an ordinal response y, suggested byAgresti andKateri (2017) and developed in amore general context by Thas et al. (2012).”
- Bias-Reduced Doubly Robust Estimation (2015, methodology): “Thas et al. (2012) show that τ̂ n is asymptotically normal with mean τ and covariance matrix Σ(τ ) which can be consistently estimated using the sandwich estimator”
- Rank‐based procedures in factorial designs: hypotheses about non‐parametric treatment effects (2016, methodology): “Recently, Fan and Zhang (2014, 2015) have proposed a generalized estimating equations approach for rank-transformed data and Thas et al. (2012) and De Neve and Thas (2015) have introduced the similar concept of the so-called probabilistic index model (PIM).”