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In this paper, we consider the Zenga index, one of the most recent inequality index. We keep the finite-valued original form and address the asymptotic theory. The asymptotic normality is established through a multinomial representation. The Influence function is also given. Th results are simulated and applied to Senegalese data., 20 pages

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen nonparametric estimators of the probability density functions whose discrepancy is estimated, we use the wavelets approach and the geometry of Besov spaces. One-sided and two-sided statistical tests are derived as well as symmetrized estimators. Almost sure rates of convergence and asymptotic normality theorem are obtained in the general case, and next particularized for the Renyi and Tsallis families and for the Kullback-Leibler measure as well. The applicability of the results to usual distribution functions is addressed., Comment: 33 pages

In this paper we establish asymptotic simultaneous confidence bands for the transformation kernel estimator of copulas introduced in Omelka et al.(2009). To this aim, we prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation, under smoothness conditions on the copula function. We also study the bias, which tends asymptotically and uniformly to zero with the same precise rate. Some simulation experiments are finally provided to support our results, Comment: 5

We prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of kernel copula estimators from their expectations. We deal especially with the \textit{local linear}, the \textit{mirror-reflection} and the \textit{transformation} estimators. These results are useful for establishing the strong uniform in bandwidth consistency of these kernel estimators., Comment: 15