{
  "id": "1108.5346",
  "version": "v1",
  "published": "2011-08-26T16:17:41.000Z",
  "updated": "2011-08-26T16:17:41.000Z",
  "title": "Constructive quantization: approximation by empirical measures",
  "authors": [
    "Steffen Dereich",
    "Michael Scheutzow",
    "Reik Schottstedt"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we study the approximation of a probability measure $\\mu$ on $\\mathbb{R}^{d}$ by its empirical measure $\\hat{\\mu}_{N}$ interpreted as a random quantization. As error criterion we consider an averaged $p$-th moment Wasserstein metric. In the case where $2p<d$, we establish refined upper and lower bounds for the error, a high-resolution formula. Moreover, we provide a universal estimate based on moments, a so-called Pierce type estimate. In particular, we show that quantization by empirical measures is of optimal order under weak assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-26T16:17:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F25",
      "65D23"
    ],
    "keywords": [
      "empirical measure",
      "constructive quantization",
      "approximation",
      "th moment wasserstein metric",
      "pierce type estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5346D"
    }
  }
}