{
  "id": "2302.01121",
  "version": "v1",
  "published": "2023-02-02T14:25:36.000Z",
  "updated": "2023-02-02T14:25:36.000Z",
  "title": "Comparing regression curves -- an $L^1$-point of view",
  "authors": [
    "Patrick Bastian",
    "Holger Dette",
    "Lukas Koletzko",
    "Kathrin Möllenhoff"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-02T14:25:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regression curves",
      "finite sample properties",
      "asymptotic confidence intervals",
      "small simulation study",
      "bootstrap methodology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}