Comparing regression curves -- an $L^1$-point of view

TL;DR

This paper introduces methods for comparing regression curves using the $L^1$-distance, developing confidence intervals, hypothesis tests, and bootstrap procedures to assess their similarity with proven theoretical properties.

Contribution

It presents novel asymptotic confidence intervals, equivalence tests, and a bootstrap approach tailored for $L^1$-distance comparison of regression curves.

Findings

Bootstrap method shows good finite sample performance.

Asymptotic confidence intervals are rigorously validated.

Statistical tests effectively assess curve similarity.

Abstract

In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study.