Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data

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 the associated Lorenz process is established under appropriate assumptions. Using this strong Gaussian approximation, a law of the iterated logarithm for the Lorenz process is also derived.