{
  "id": "0904.3295",
  "version": "v1",
  "published": "2009-04-21T17:12:40.000Z",
  "updated": "2009-04-21T17:12:40.000Z",
  "title": "A Bernstein-type inequality for suprema of random processes with an application to statistics",
  "authors": [
    "Yannick Baraud"
  ],
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We use the generic chaining device proposed by Talagrand to establish exponential bounds on the deviation probability of some suprema of random processes. Then, given a random vector $\\xi$ in $\\R^{n}$ the components of which are independent and admit a suitable exponential moment, we deduce a deviation inequality for the squared Euclidean norm of the projection of $\\xi$ onto a linear subspace of $\\R^{n}$. Finally, we provide an application of such an inequality to statistics, performing model selection in the regression setting when the errors are possibly non-Gaussian and the collection of models possibly large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-21T17:12:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70",
      "62G08"
    ],
    "keywords": [
      "random processes",
      "bernstein-type inequality",
      "application",
      "statistics",
      "establish exponential bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.3295B"
    }
  }
}