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Comparing regression curves: an L1-point of view

Author

Listed:
  • Patrick Bastian

    (Ruhr-Universität Bochum)

  • Holger Dette

    (Ruhr-Universität Bochum)

  • Lukas Koletzko

    (Ruhr-Universität Bochum)

  • Kathrin Möllenhoff

    (Heinrich-Heine-Universität Düsseldorf)

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.

Suggested Citation

  • Patrick Bastian & Holger Dette & Lukas Koletzko & Kathrin Möllenhoff, 2024. "Comparing regression curves: an L1-point of view," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(1), pages 159-183, February.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:1:d:10.1007_s10463-023-00880-8
    DOI: 10.1007/s10463-023-00880-8
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    References listed on IDEAS

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    1. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    2. Holger Dette & Kathrin Möllenhoff & Stanislav Volgushev & Frank Bretz, 2018. "Equivalence of Regression Curves," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 711-729, April.
    3. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    4. Ostrovski, Vladimir, 2017. "Testing equivalence of multinomial distributions," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 77-82.
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