Distributional (Single) Index Models

A Distributional (Single) Index Model (DIM) is a semiparametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single-index models for the estimation of the conditional mean of a response given covariates, and isotonic distributional regression. The model for the index is parametric, whereas the conditional distributions are estimated nonparametrically under a stochastic ordering constraint. We show consistency of our estimators and apply them to a highly challenging dataset on the length of stay (LoS) of patients in intensive care units. We use the model to provide skillful and calibrated probabilistic predictions for the LoS of individual patients, which outperform the available methods in the literature.