{
  "id": "1111.4591",
  "version": "v1",
  "published": "2011-11-19T22:29:05.000Z",
  "updated": "2011-11-19T22:29:05.000Z",
  "title": "Empirical Quantile CLTs for Time Dependent Data",
  "authors": [
    "James Kuelbs",
    "Joel Zinn"
  ],
  "comment": "52 pages",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We establish empirical quantile process CLTs based on $n$ independent copies of a stochastic process $\\{X_t: t \\in E\\}$ that are uniform in $t \\in E$ and quantile levels $\\alpha \\in I$, where $I$ is a closed sub-interval of $(0,1)$. Typically $E=[0,T]$, or a finite product of such intervals. Also included are CLT's for the empirical process based on $\\{I_{X_t \\le y} - \\rm {Pr}(X_t \\le y): t \\in E, y \\in R \\}$ that are uniform in $t \\in E, y \\in R$. The process $\\{X_t: t \\in E\\}$ may be chosen from a broad collection of Gaussian processes, compound Poisson processes, stationary independent increment stable processes, and martingales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-19T22:29:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F17",
      "62E20"
    ],
    "keywords": [
      "time dependent data",
      "empirical quantile clts",
      "empirical quantile process clts",
      "stationary independent increment stable processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4591K"
    }
  }
}