A Distributional (Single) Index Model (DIM) is a semi-parametric 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 non-parametrically under a stochastic ordering constraint. We show consistency of our estimators and apply them to a highly challenging data set 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, that outperform the available methods in the literature.

翻译：分布(单)指数模型(DIM)是分布回归的半参数模型,即对有条件分布给定的共变数的估计。该方法结合了古典单一指数模型,用于估计一个响应给定的有条件平均值,以及等离子分布回归。该指数的模型是参数,而有条件分布是在随机排序限制下非对称估计的。我们显示了我们的估计数据的一致性,并将其应用到关于特护单位病人停留时间(LOS)的一组极具挑战性的数据中。我们使用该模型为个别病人的LOS提供熟练和校准的概率预测,这些预测超过了文献中的现有方法。