An efficient estimator for Gibbs random fields

Martin Janžura

Kybernetika (2014)

  • Volume: 50, Issue: 6, page 883-895
  • ISSN: 0023-5954

Abstract

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An efficient estimator for the expectation ∫ f P ̣ is constructed, where P is a Gibbs random field, and f is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.

How to cite

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Janžura, Martin. "An efficient estimator for Gibbs random fields." Kybernetika 50.6 (2014): 883-895. <http://eudml.org/doc/262168>.

@article{Janžura2014,
abstract = {An efficient estimator for the expectation $\int f P̣$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.},
author = {Janžura, Martin},
journal = {Kybernetika},
keywords = {Gibbs random field; efficient estimator; empirical estimator; Gibbs random field; efficient estimator; empirical estimator},
language = {eng},
number = {6},
pages = {883-895},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An efficient estimator for Gibbs random fields},
url = {http://eudml.org/doc/262168},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Janžura, Martin
TI - An efficient estimator for Gibbs random fields
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 6
SP - 883
EP - 895
AB - An efficient estimator for the expectation $\int f P̣$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.
LA - eng
KW - Gibbs random field; efficient estimator; empirical estimator; Gibbs random field; efficient estimator; empirical estimator
UR - http://eudml.org/doc/262168
ER -

References

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  5. Greenwood, P. E., Wefelmeyer, W., 10.1214/aos/1176324459, Ann. Statist. 23 (1995), 132-143. Zbl0822.62067MR1331660DOI10.1214/aos/1176324459
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  8. Hájek, J., 10.1007/BF00533669, Wahrsch. Verw. Gebiete 14 (1970), 323-330. Zbl0193.18001MR0283911DOI10.1007/BF00533669
  9. Janžura, M., Statistical analysis of Gibbs random fields., In: Trans. 10th Prague Conference on Inform. Theory, Stat. Dec. Functions, Random Processes, Prague 1984, pp. 429-438. Zbl0708.62092MR1136301
  10. Janžura, M., Local asymptotic normality for Gibbs random fields., In: Proc. Fourth Prague Symposium on Asymptotic Statistics (P. Mandl and M. Hušková, eds.), Charles University, Prague 1989, pp. 275-284. Zbl0697.62091MR1051446
  11. Janžura, M., Asymptotic behaviour of the error probabilities in the pseudo-likelihood ratio test for Gibbs-Markov distributions., In: Prof. Asymptotic Statistics (P. Mandl and M. Hušková, eds.), Physica-Verlag, Heidelberg 1994, pp. 285-296. MR1311947
  12. Janžura, M., Asymptotic results in parameter estimation for Gibbs random fields., Kybernetika 33 (1997), 2, 133-159. Zbl0962.62092MR1454275
  13. Janžura, M., On the concept of the asymptotic Rényi distances for random fields., Kybernetika 35 (1999), 3, 353-366. Zbl1274.62061MR1704671
  14. Künsch, H., 10.1007/BF01208568, Comm. Math. Phys. 84 (1982), 207-222. MR0661133DOI10.1007/BF01208568
  15. Younes, L., 10.1007/BF00341287, Probab. Theory Rel. Fields 82 (1989), 625-645. MR1002904DOI10.1007/BF00341287

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