The paper introduces a new method for nonparametric estimation of mixing distributions, which is a generalization of the maximum likelihood estimation (MLE) of Lindsay [1,2]. The method aims at minimizing a function, named entropic risk measure, of one parameter. The authors show that by choosing a good range for this parameter, the method generalizes better (less prone to overfitting) than the maximum likelihood method. Tests are conducted with a synthetic set of data from a 2D Gaussian mixture distribution. The paper also discusses the relationship between the introduced method and the rate-distortion method.

This is a fairly technical paper: easy to read for theoreticians in the field (mathematicians, statisticians), but extremely hard for the rest of the world to understand since deep knowledge of statistical distribution literature is required. Also, note that the proposed method has been proved for synthetic data of a certain distribution; there is not yet proof of its workability in real-world data.