Constructing Simultaneous Confidence Bands for Errors-in-variables Curves with Application to the Lorenz Curve

Abstract: Errors-in-variables curves are curves where errors exist not only in the independent variable but also in the dependent variable. We address the challenge of constructing simultaneous confidence bands (SCBs) for such curves. Our method finds application in the Lorenz curve, which represents the concentration of income or wealth. Unlike ordinary regression curves, the Lorenz curve incorporates errors in its explanatory variable and requires a fundamentally different treatment. To the best of our knowledge, the development of SCBs for such curves has not been explored in previous research. Using the Lorenz curve as a case study, this paper proposes a novel approach to address this challenge.