{
  "id": "math/0604197",
  "version": "v2",
  "published": "2006-04-09T04:49:42.000Z",
  "updated": "2008-04-21T06:11:35.000Z",
  "title": "Two non-regular extensions of large deviation bound",
  "authors": [
    "Masahito Hayashi"
  ],
  "comment": "This manusript is shortened version of the previouse manuscript",
  "categories": [
    "math.PR"
  ],
  "abstract": "We formulate two types of extensions of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval estimation. Both coincide in the regular case, but do not necessarily coincide in a non-regular case. Using the limits of relative R\\'{e}nyi entropies, we derive their upper bounds and give a necessary and sufficient condition for the coincidence of the two upper bounds. We also discuss the attainability of these two bounds in several non-regular location shift families.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-21T06:11:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation bound",
      "non-regular extensions",
      "non-regular location shift families",
      "upper bounds",
      "point estimation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4197H"
    }
  }
}