An automatic procedure to determine groups of nonparametric regression curves

TL;DR

This paper introduces an automatic testing procedure for grouping nonparametric regression curves, enabling efficient identification of similar curve groups with an automatic selection of their number, demonstrated through simulations and a tunnel geometry case study.

Contribution

It presents a novel automatic method for grouping nonparametric regression curves with an integrated procedure to determine the optimal number of groups.

Findings

The method effectively identifies groups in simulated data.

Application to tunnel cross-sections reveals heterogeneity in geometry.

Finite sample properties are favorable compared to existing methods.

Abstract

In many situations it could be interesting to ascertain whether nonparametric regression curves can be grouped, especially when confronted with a considerable number of curves. The proposed testing procedure allows to determine groups with an automatic selection of their number. A simulation study is presented in order to investigate the finite sample properties of the proposed methods when compared to existing alternative procedures. Finally, the applicability of the procedure to study the geometry of a tunnel by analysing a set of cross-sections is demonstrated. The results obtained show the existence of some heterogeneity in the tunnel geometry.