Amor Keziou

Parametric estimation and tests through divergences and the duality technique

We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple and composite hypotheses, extending the maximum likelihood technique. Another view of the maximum likelihood approach, for estimation and tests, is given. We prove existence and consistency of the proposed estimates. The limit laws of the estimates and test statistics (including the generalized likelihood ratio one) are given under both the null and the alternative hypotheses, and approximations of the power functions are deduced. A new procedure of construction of confidence regions, when the parameter may be a boundary value of the parameter space, is proposed. Also, a solution to the irregularity problem of the generalized likelihood ratio test pertaining to the number of components in a mixture is given, and a new test is proposed, based on @g^2-divergence on signed finite measures and the duality technique.

Is organic matter alone sufficient to predict isoproturon sorption in calcareous soils

Eleven soils collected from Champagne-Ardenne area (France) were used to investigate isoproturon sorption in laboratory conditions. Our results identified the organic matter (OM) and the ratio of calcite content to OM content (Rt) as the main two parameters governing isoproturon retention in soils. While organic matter favored pesticide sorption, calcite had an antagonistic effect since it limited isoproturon retention. The Rt ratio of calcite content to organic matter content in soils appeared to be a parameter that should be considered in predictive models in addition to OM in regions presenting calcareous soils. Adsorption of isoproturon as a function of Rt and OM was successfully described through a simple empirical model.

A test of independence in some copula models

The purpose of this paper is to provide limit laws for semiparametric estimators of copulas. Some statistical tests of independence are introduced as a consequence of this methodology. We are primarily concernedwith the case where the parameter lies on the boundary of the admissible domain.

A New Test Procedure of Independence in Copula Models via χ2-Divergence

We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of χ2-divergence on signed finite measures. The asymptotic properties of the proposed estimate and the test statistic are studied under the null and alternative hypotheses, with simple and standard limit distributions both when the parameter is an interior point or not.

New Entropy Estimator with an Application to Test of Normality

In the present article, we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed.

Generalized Mutual-Information Based Independence Tests

We derive independence tests by means of dependence measures thresholding in a semiparametric context. Precisely, estimates of mutual information associated to \(\varphi \)-divergences are derived through the dual representations of \(\varphi \)-divergences. The asymptotic properties of the estimates are established, including consistency, asymptotic distribution and large deviations principle. The related tests of independence are compared through their relative asymptotic Bahadur efficiency and numerical simulations.