Electronic Journal of Statistics

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

P. Vandekerkhove, J. M. Padbidri, and D. L. McDowell

Full-text: Open access

Abstract

In this paper, we consider the problem of selecting the most appropriate model, amongst 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 the Expectation-Maximization (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. We state, under mild conditions, that our estimator of the $ICE$ distance converges at the rate $\sqrt{n}$ in probability along with the consistency of our model selection procedure (ability to detect asymptotically the right model). The $ICE$ criterion shows, over a set of benchmark examples, numerically improved performance from the existing distance-based criteria in identifying the correct model. The method is applied in a material fatigue life context to model the distribution of indicators of the fatigue crack formation potency, obtained from numerical experiments.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 3141-3175.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1421936897

Digital Object Identifier
doi:10.1214/15-EJS985

Mathematical Reviews number (MathSciNet)
MR3303680

Zentralblatt MATH identifier
1308.62134

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62E10: Characterization and structure theory

Keywords
EM algorithm extreme value Gumbel mixture model selection metal fatigue quasi-maximum likelihood probability distance

Citation

Vandekerkhove, P.; Padbidri, J. M.; McDowell, D. L. Integrated Cumulative Error (ICE) distance for non-nested mixture model selection: Application to extreme values in metal fatigue problems. Electron. J. Statist. 8 (2014), no. 2, 3141--3175. doi:10.1214/15-EJS985. https://projecteuclid.org/euclid.ejs/1421936897


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