Nonparametric density estimation with region-censored data

The paper proposes a new Maximum Entropy estimator for non-parametric density estimation from region censored observations in the context of population studies, where standard Maximum Likelihood is affected by over-fitting and non-uniqueness problems. The link between Maximum Entropy and Maximum Likelihood estimation for the exponential family has often been invoked in the literature. When, as it is the case for censored observations, the constraints on the Maximum Entropy estimator are derived from independent observations of a set of non-linear functions, this link is lost increasing the difference between the two criteria. By combining the two criteria we propose a novel density estimator that is able to overcome the singularities of the Maximum Likelihood estimator while maintaining a good fit to the observed data, and illustrate its behavior in real data (hyperbaric diving).