A distribution-free tracking interval for model selection: application in the strength of brittle materials

Abstract

In the literature of model selection, Vuong’s test and Akaike information criterion aim to find the best statistical model. Both of them are related to the expectation of the log-likelihood function of the rival models, but they are not sensitive to the small difference between rival models. The goal of this study is to develop a simple model selection approach which does not assume a true distribution for data. We have introduced a nonparametric tracking interval in the context of model selection. We have shown that this interval is compatibale with the known Vuong’s test results, but here we let the magnitude of the data enhance the performance of statistical inference. Simulation study provide this method works well. It is shown that this interval has acceptable results for classical densities, autoregressive models and finite mixture models. This tracking interval is illustrated on a real data. The strength(mechanics) of brittle materials in various applications is characterized by Weibull distribution. These kind of data are usually skewed and platykurtic or leptokurtic. Thus, their median is more precise than their mean. Using the proposed interval, it is shown that, sometimes the Gamma and Log-normal distributions are suitable alternative to Weibull distribution.