Integrated Cumulative Error (ICE) distance for non-nested mixture model selection: Application to extreme values in metal fatigue problems

In this paper, we consider the problem of selecting the most appropriate model, among a given collection of mixture models, to describe datasets likely drawn from mixture of distributions. The proposed method consists of finding the quasi-maximum likelihood estimators (QMLEs) of the various models in competition, using ExpectationMaximization (EM) type algorithms, and subsequently estimating, for every model, a statistical distance to the true model based on the empirical cumulative distribution function (cdf) of the original dataset and the QMLE-fitted cdf. To evaluate the goodness of fit, a new metric, the Integrated Cumulative Error (ICE) is proposed and compared with other existing metrics for accuracy of detecting the appropriate model.