{
  "id": "1312.6489",
  "version": "v4",
  "published": "2013-12-23T09:13:49.000Z",
  "updated": "2015-05-20T14:08:41.000Z",
  "title": "New Algorithms for $M$-Estimation of Multivariate Location and Scatter",
  "authors": [
    "Lutz Duembgen",
    "Klaus Nordhausen",
    "Heike Schuhmacher"
  ],
  "categories": [
    "stat.CO"
  ],
  "abstract": "We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and devise a partial Newton-Raphson procedure. In connection with symmetrized $M$-estimators we work with incomplete $U$-statistics to accelerate our procedures initially.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-01-28T18:03:03.000Z",
      "abstract": "We present new algorithms for $M$-estimators of multivariate location and scatter and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and devise a partial Newton-Raphson procedure. In connection with the symmetrized $M$-estimators we work with incomplete $U$-statistics to accelerate our procedures initially.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-05-20T14:08:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62H12",
      "65C60"
    ],
    "keywords": [
      "multivariate location",
      "estimation",
      "second order taylor expansion",
      "partial newton-raphson procedure",
      "estimators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6489D"
    }
  }
}