{
  "id": "0902.4796",
  "version": "v1",
  "published": "2009-02-27T10:48:27.000Z",
  "updated": "2009-02-27T10:48:27.000Z",
  "title": "A Berry--Esseen theorem for sample quantiles under weak dependence",
  "authors": [
    "S. N. Lahiri",
    "S. Sun"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AAP533 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 1, 108-126",
  "doi": "10.1214/08-AAP533",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper proves a Berry--Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be $O(n^{-1/2})$ as $n\\to\\infty$, where $n$ denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate $O(n^{-1/2})$ is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series data often are heavy-tailed and quantile based methods play an important role in various problems in finance, including hedging and risk management.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-27T10:48:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60G10",
      "62E20"
    ],
    "keywords": [
      "sample quantiles",
      "berry-esseen theorem",
      "weak dependence",
      "strongly-mixing random variables",
      "financial time series data"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4796L"
    }
  }
}