{
  "id": "2104.03479",
  "version": "v1",
  "published": "2021-04-08T02:43:03.000Z",
  "updated": "2021-04-08T02:43:03.000Z",
  "title": "Berry--Esseen bounds for generalized $U$ statistics",
  "authors": [
    "Zhuo-Song Zhang"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we establish optimal Berry--Esseen bounds for the generalized $U$-statistics. The proof is based on a new Berry--Esseen theorem for exchangeable pair approach by Stein's method under a general linearity condition setting. As applications, an optimal convergence rate of the normal approximation for subgraph counts in Erd\\\"os--R\\'enyi graphs and graphon-random graph is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-08T02:43:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05"
    ],
    "keywords": [
      "statistics",
      "establish optimal berry-esseen bounds",
      "optimal convergence rate",
      "graphon-random graph",
      "normal approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}