{
  "id": "1206.6721",
  "version": "v2",
  "published": "2012-06-28T15:09:16.000Z",
  "updated": "2013-01-04T14:13:32.000Z",
  "title": "Quasi-Likelihood and/or Robust Estimation in High Dimensions",
  "authors": [
    "Sara van de Geer",
    "Patric Müller"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/12-STS397 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Statistical Science 2012, Vol. 27, No. 4, 469-480",
  "doi": "10.1214/12-STS397",
  "categories": [
    "math.ST",
    "stat.ME",
    "stat.TH"
  ],
  "abstract": "We consider the theory for the high-dimensional generalized linear model with the Lasso. After a short review on theoretical results in literature, we present an extension of the oracle results to the case of quasi-likelihood loss. We prove bounds for the prediction error and $\\ell_1$-error. The results are derived under fourth moment conditions on the error distribution. The case of robust loss is also given. We moreover show that under an irrepresentable condition, the $\\ell_1$-penalized quasi-likelihood estimator has no false positives.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-04T14:13:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "robust estimation",
      "high dimensions",
      "high-dimensional generalized linear model",
      "fourth moment conditions",
      "penalized quasi-likelihood estimator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6721V"
    }
  }
}