This study uses a Monte Carlo simulation design to assess the performance of Beta and linear mixed models on bounded response variables through comparison of four estimation methods. Four factors affecting the performance of the estimation methods were considered: the number of groups, the number of observations per group, the variance and distribution of the random effects. Our results showed that, for small number of groups (less than 30), the Beta mixed model outperformed the linear mixed model whatever the size of the groups. In the case of a large number of groups (superior or equal to 30), both approaches showed relatively close performance. The results from the simulation study have been illustrated with real life data.

In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly consistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an asymptotically standard normal test for model selection. The Monte Carlo simulation show the effectiveness of the proposed estimation methods and statistical tests.

In this paper, we study a bias reduced kernel density estimator and derive a nonparametric \(\phi\)-divergence estimator based on this density estimator. We investigate the asymptotic properties of these two estimators and we formulate an asymptotically standard normal test for model selection.

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This paper discusses choice procedures that select the set of best alternatives taking into account reflexive binary relations (called pseudo tournaments in the paper), such as those that can be obtained when constructing an outranking relation `a' la Electre. The paper contains interesting results which link together the second exploitation step in the Electre I outranking method with two choice procedures (Gocha and Getcha choice procedures also known in the literature as Schwartz set and Smith set respectively). A set of results that characterize some properties of the two outranking methods (ElectI and ElectIP choice procedures) is also presented.