Empiricial Comparison between Some Model Selection Criteria

Model selection aims to find the best model. Most of the usual criteria are based on goodness of fit and parsimony and aim to maximize a transformed version of likelihood. The situation is less clear when two models are equivalent: are they close to the unknown true model or are they far from it? Based on simulations, we study the results of Vuong's test, Cox's test, AIC and BIC and the ability of these four tests to discriminate between models.     

Tracking interval for selecting between non-nested models: An investigation for Type II right censored data

In this paper, we consider the setting where the observed data is incomplete. For the general situation where the number of gaps as well as the number of unobserved values in some gaps go to infinity, the asymptotic behavior of maximum likelihood estimator is not clear. We derive and investigate the asymptotic properties of maximum likelihood estimator under censorship and drive a statistic for testing the null hypothesis that the proposed non-nested models are equally close to the true model against the alternative hypothesis that one model is closer when we are faced with a life-time situation. Furthermore rewrite a normalization of a difference of Akaike criterion for estimating the difference of expected Kullback–Leibler risk between the distributions in two different models.     

Model selection using union-intersection principle for non nested models

In this article, we have extended the Vuong’s (1989 Vuong, Q.H. (1989). Likelihood ratio tests for model selection and non-nested hypothesis. Econometrica. 57:307–333.[Crossref], [Web of Science ®] , [Google Scholar]) model selection test to three models in accordance to union-intersection principle. Using the Kullback–Leibler criterion to measure the closeness of a model to the truth, we propose a simple likelihood ratio-based statistics for testing the null hypothesis that the competing models are equally close to the true data-generating process against the alternative hypothesis that at least one model is closer. We show that the distribution of the test statistic is asymptotically equal to the distribution of the maximum of dependent random variables with bivariate folded standard normal distribution. The density function of the maximum of dependent random variables with elliptically contoured distributions has been obtained by other researchers, but, not for distributions which do not belong to the elliptically contoured distributions family. In this article, the exact distribution of the maximum of dependent random variables with bivariate folded standard normal distribution is calculated as an asymptotic distribution of the proposed test statistic. The test is directional and is derived successively for the cases where the competing models are non nested and whether three, two, one, or none of them are misspecified.     

Non parametric multiple comparisons of non nested rival models

The practice for testing homogeneity of several rival models is of interest. In this article, we consider a non parametric multiple test for non nested distributions in the context of the model selection. Based on the linear sign rank test, and the known union–intersection principle, we let the magnitude of the data to give a better performance to the test statistic. We consider the sample and the non nested rival models as blocks and treatments, respectively, and introduce the extended Friedman test version to compare with the results of the test based on the linear sign rank test. A real dataset based on the waiting time to earthquake is considered to illustrate the results.     

Linear Signed Rank Test for Model Selection

In this article, we consider a linear signed rank test for non-nested distributions in the context of the model selection. Introducing a new test, we show that, it is asymptotically more efficient than the Vuong test and the test statistic based on B statistic introduced by Clarke. However, here, we let the magnitude of the data give a better performance to the test statistic. We have shown that this test is an unbiased one. The results of simulations show that the rank test has the greater statistical power than the Vuong test where the underline distributions is symmetric.