{
  "id": "2102.04923",
  "version": "v1",
  "published": "2021-02-09T16:29:52.000Z",
  "updated": "2021-02-09T16:29:52.000Z",
  "title": "Berry--Esseen Bounds for Multivariate Nonlinear Statistics with Applications to M-estimators and Stochastic Gradient Descent Algorithms",
  "authors": [
    "Qi-Man Shao",
    "Zhuo-Song Zhang"
  ],
  "comment": "53 pages",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best possible for many known statistics. As applications, Berry--Esseen bounds for M-estimators and averaged stochastic gradient descent algorithms are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-09T16:29:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "62E20",
      "62F12"
    ],
    "keywords": [
      "berry-esseen bound",
      "m-estimators",
      "applications",
      "averaged stochastic gradient descent algorithms",
      "general multivariate nonlinear statistics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}