Statistical Modelling under Epistemic Data Imprecision: Some Results on Estimating Multinomial Distributions and Logistic Regression for Coarse Categorical Data

The paper deals with parameter estimation for categorical data under epistemic data imprecision, where for a part of the data only coarse(ned) versions of the true values are observable. For different observation models formalizing the information available on the coarsening process, we derive the (typically set-valued) maximum likelihood estimators of the underlying distributions. We discuss the homogeneous case of independent and identically distributed variables as well as logistic regression under a categorical covariate. We start with the imprecise point estimator under an observation model describing the coarsening process without any further assumptions. Then we determine several sensitivity parameters that allow the refinement of the estimators in the presence of auxiliary information.