Bootstrap non-nested mixture model selection - Application to extreme value modeling in metal fatigue problems

Pierre Vandekerkhove (1) , Jagan Padbiri (2) , David Mcdowell (2, 3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 George W. Woodruff School of Mechanical Engineering
3 IPST - Institute for materials

In this paper, we consider the problem of selecting the most appropriate model from many possible models to describe datasets involving mixtures of distributions. The proposed method consists of finding the maximul likelihood estimators (MLEs) of different assumed mixture models that describe a dataset, using the Expectation- Maximization (EM) algorithm, and subsequently using bootstrap sampling technique to identify the distance between the empirical cumulative distribution function (cdf) of the dataset and the MLE fitted cdf. To test 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. The ICE metric shows a markedly improved performance, from the existing metrics, in identifying the correct mixture model. The method is applied to model the distribution of indicators of the fatigue crack formation potency, obtained from numerical experiments.

Mots clés: Model choice; bootstrap; mixture; Gumbel; Gaussian; extreme; metal fatigue

Domaines: Applications [stat.AP]

Pierre Vandekerkhove, Jagan Padbiri, David Mcdowell. Bootstrap non-nested mixture model selection - Application to extreme value modeling in metal fatigue problems. 2013. ⟨hal-00796645v2⟩