Comparing regression curves: an L1-point of view

Patrick Bastian (), Holger Dette (), Lukas Koletzko () and Kathrin Möllenhoff ()
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Patrick Bastian: Ruhr-Universität Bochum
Holger Dette: Ruhr-Universität Bochum
Lukas Koletzko: Ruhr-Universität Bochum
Kathrin Möllenhoff: Heinrich-Heine-Universität Düsseldorf

Annals of the Institute of Statistical Mathematics, 2024, vol. 76, issue 1, No 9, 159-183

Abstract: Abstract In this paper, we compare two regression curves by measuring their difference by the area between the two curves, represented by their $$L^1$$ 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.

Keywords: Equivalence testing; Comparison of curves; Bootstrap; Directional Hadamard differentiability (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10463-023-00880-8

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