{
  "id": "0901.2468",
  "version": "v1",
  "published": "2009-01-16T12:31:52.000Z",
  "updated": "2009-01-16T12:31:52.000Z",
  "title": "The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization",
  "authors": [
    "Wei-Dong Liu",
    "Zhengyan Lin",
    "Qi-Man Shao"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/08-AAP527 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 2008, Vol. 18, No. 6, 2337-2366",
  "doi": "10.1214/08-AAP527",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\mathbf{X}_1,...,\\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^{\\alpha}\\leq p\\leq c_2n^{\\alpha}$ for some positive constants $c_1,c_2$ and $\\alpha$. In this paper we introduce a new statistic for testing independence of the $p$-variates of the population and prove that the limiting distribution is the extreme distribution of type I with a rate of convergence $O((\\log n)^{5/2}/\\sqrt{n})$. This is much faster than $O(1/\\log n)$, a typical convergence rate for this type of extreme distribution. A simulation study and application to stochastic optimization are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-16T12:31:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "62F05"
    ],
    "keywords": [
      "stochastic optimization",
      "high dimension",
      "berry-esseen bound",
      "asymptotic distribution",
      "independence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}