{
  "id": "2102.06379",
  "version": "v1",
  "published": "2021-02-12T07:53:22.000Z",
  "updated": "2021-02-12T07:53:22.000Z",
  "title": "Central Limit Theorems for General Transportation Costs",
  "authors": [
    "Eustasio del Barrio",
    "Alberto González-Sanz",
    "Jean-Michel Loubes"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport maps and potentials for a large class of costs in R d. We derive a central limit theorem (CLT) towards a Gaussian distribution for the empirical transportation cost under minimal assumptions, with a new proof based on the Efron-Stein inequality and on the sequential compactness of the closed unit ball in L 2 (P) for the weak topology. We provide also CLTs for empirical Wassertsein distances in the special case of potential costs | $\\bullet$ | p , p > 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-12T07:53:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "general transportation costs",
      "general target probability",
      "optimal transport maps",
      "empirical transportation cost"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}