{
  "id": "1411.3083",
  "version": "v1",
  "published": "2014-11-12T06:20:43.000Z",
  "updated": "2014-11-12T06:20:43.000Z",
  "title": "On limiting distribution of U-statistics based on associated random variables",
  "authors": [
    "Mansi Garg",
    "Isha Dewan"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let $\\lbrace X_n, n \\ge 1 \\rbrace$ be a sequence of stationary associated random variables. Based on this sample, we establish a central limit theorem for U-statistics with monotonic kernels of degree 3 and above using the Hoeffding's decomposition. We also extend these results to U-statistics based on non-monotonic functions. We also obtain a consistent estimator of $\\sigma_f$, where $\\sigma_f^2 = \\underset{n \\to \\infty}{lim}(Var S_n)/n$, $S_n = \\sum_{j=1}^n f(X_j)$, and $f$ is a non-monotonic function, using the ideas of Peligrad and Suresh $(1995)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-12T06:20:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limiting distribution",
      "u-statistics",
      "non-monotonic function",
      "stationary associated random variables",
      "central limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.3083G"
    }
  }
}