{
  "id": "0911.1164",
  "version": "v2",
  "published": "2009-11-06T02:02:04.000Z",
  "updated": "2011-05-16T08:44:09.000Z",
  "title": "Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo",
  "authors": [
    "Yves F. Atchadé"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/10-AOS828 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Statistics 2011, Vol. 39, No. 2, 990-1011",
  "doi": "10.1214/10-AOS828",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.CO",
    "stat.TH"
  ],
  "abstract": "We study the asymptotic behavior of kernel estimators of asymptotic variances (or long-run variances) for a class of adaptive Markov chains. The convergence is studied both in $L^p$ and almost surely. The results also apply to Markov chains and improve on the existing literature by imposing weaker conditions. We illustrate the results with applications to the $\\operatorname {GARCH}(1,1)$ Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-16T08:44:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adaptive markov chain monte carlo",
      "asymptotic variance",
      "kernel estimators",
      "bayesian logistic regression",
      "asymptotic behavior"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Institute of Mathematical Statistics",
      "journal": "Ann. Stat."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.1164A"
    }
  }
}