{
  "id": "1503.03393",
  "version": "v1",
  "published": "2015-03-11T15:57:25.000Z",
  "updated": "2015-03-11T15:57:25.000Z",
  "title": "Asymptotic properties of one-step $M$-estimators based on nonidentically distributed observations and applications to some regression problems",
  "authors": [
    "Yu. Yu. Linke"
  ],
  "comment": "in Russian",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These estimators generalize Fisher's one-step approximations to consistent maximum likelihood estimators. Sufficient conditions are presented for asymptotic normality of the one-step $M$-estimators under consideration. As a consequence, we consider some well-known nonlinear regression models where the procedure mentioned allow us to construct explicit asymptotically optimal estimators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-11T15:57:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62F12",
      "62J02"
    ],
    "keywords": [
      "nonidentically distributed observations",
      "regression problems",
      "asymptotic properties",
      "identically distributed random variables",
      "construct explicit asymptotically optimal estimators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150303393L"
    }
  }
}