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

TL;DR

This paper develops a novel method for constructing simultaneous confidence bands for errors-in-variables curves, exemplified by the Lorenz curve, addressing a previously unexplored statistical challenge.

Contribution

It introduces the first approach for SCBs in errors-in-variables curves, specifically applied to the Lorenz curve, accounting for errors in both variables.

Findings

Proposed a new method for errors-in-variables curves

Applied the method to Lorenz curve analysis

Addressed a gap in existing statistical techniques

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.