the purpose of this paper is to provide some asymptotic results for nonparametric estimator of the lorenz curve and lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. first, we show that nonparametric estimator of the lorenz curve is uniformly strongly consistent for the associated lorenz curve. also, a strong gaussian approximation for ...

Résumé Nous prouvons le propriétés de grandes déviations (P.G.D.) pour les mesures empiriques en τ -topologie, dans les cas de suites stationnaires sous conditions de mélange α(n) exp(−n(log n)1+δ) pour certain δ > 0, ou φ(n) exp(−n`(n)) avec `(n)→∞. Les examples de châınes de Markov récurrentes au sense de Doeblin montrent que ces conditions ne permettrent pas de amélioration substantielle, et...

The strong mixing property for a sequence of random variables is interesting in its own right. It is discussed that under what conditions the strong mixing property holds for linear stochastic processes and in particular ARMA processes. Then an example of Non-Strong mixing Autoregressive Processes is discussed here.