A Simple Consistent Nonparametric Estimator of the Lorenz Curve

We propose a nonparametric estimator of the Lorenz curve that satisfies its theoretical properties, including monotonicity and convexity. We adopt a transformation approach that transforms a constrained estimation problem into an unconstrained one, which is estimated nonparametrically. We utilize the splines to facilitate the numerical implementation of our estimator and to provide a parametric representation of the constructed Lorenz curve. We conduct Monte Carlo simulations to demonstrate the superior performance of the proposed estimator. We apply our method to estimate the Lorenz curve of the U.S. household income distribution and calculate the Gini index based on the estimated Lorenz curve