Asymptotic results in parameter estimation for Gibbs random fields

Martin Janžura

Kybernetika (1997)

  • Volume: 33, Issue: 2, page 135-159
  • ISSN: 0023-5954

How to cite


Janžura, Martin. "Asymptotic results in parameter estimation for Gibbs random fields." Kybernetika 33.2 (1997): 135-159. <>.

author = {Janžura, Martin},
journal = {Kybernetika},
keywords = {Gibbs random fields; maximum likelihood estimators; maximum pseudo-likelihood estimators; consistency; asymptotic normality; asymptotic efficiency},
language = {eng},
number = {2},
pages = {135-159},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Asymptotic results in parameter estimation for Gibbs random fields},
url = {},
volume = {33},
year = {1997},

AU - Janžura, Martin
TI - Asymptotic results in parameter estimation for Gibbs random fields
JO - Kybernetika
PY - 1997
PB - Institute of Information Theory and Automation AS CR
VL - 33
IS - 2
SP - 135
EP - 159
LA - eng
KW - Gibbs random fields; maximum likelihood estimators; maximum pseudo-likelihood estimators; consistency; asymptotic normality; asymptotic efficiency
UR -
ER -


  1. J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. B 36 (1974), 192-226. (1974) Zbl0327.60067MR0373208
  2. J. Besag, On the statistical analysis of dirty pictures (with discussion), J. Roy. Statist. Soc. Ser. B 48 (1986), 259-302. (1986) Zbl0609.62150MR0876840
  3. E. Bolthausen, On the central limit theorem for stationary mixing random fields, Ann. Probab. 10 (1982), 1047-1050. (1982) Zbl0496.60020MR0672305
  4. F. Comets, On consistency of a class of estimators for exponential families of Markov random fields on a lattice, Ann. Statist. 20 (1992), 455-468. (1992) MR1150354
  5. R. L. Dobrushin, B. S. Nahapetian, Strong convexity of the pressure for the lattice systems of classical statistical physics, Teor. Mat. Phys. 20 (1974), 223-234. (1974) MR0468967
  6. D. Geman, S. Geman, Maximum Entropy and Bayesian Methods in Sciences and Engineering, (C. R. Smith and G. J. Erickson, eds), Kluwer, Dordrecht 1988. (1988) 
  7. S. Geman, C. Graffigne, Markov random field image models and their applications to computer vision, In: Proc. Internat. Congress Math. (A. M. Gleason ed.), Amer. Math. Soc, Providence, R. I. 1987. (1987) Zbl0665.68067MR0934354
  8. H. O. Georgii, Gibbs Measures and Phase Transitions, De Gruyter, Berlin 1988. (1988) Zbl0657.60122MR0956646
  9. B. Gidas, Consistency of maximum likelihood and pseudo-likelihood estimators for Gibbs distribution, In: Stochastic Differential Systems, Stochastic Control Theory, and Application (W. Fleming and P. L. Lions, eds., IMA Vol. Math. Appl. 10). Springer, New York 1988. (1988) MR0934721
  10. B. Gidas, Parameter estimation for Gibbs distributions. I. Fully observed data, In: Markov Random Fields: Theory and Applications (R. Chellapa and R. Jain, eds.), Academic Press, New York 1991. (1991) 
  11. L. Gross, Absence of second-order phase transition in the Dobrushin's uniqueness region, J. Statist. Phys. 27 (1981), 57-72. (1981) MR0610692
  12. X. Guyon, Estimation d'un champ par pseudo-vraisemblance conditionnelle: Etude asymptotique et application au cas Markovien, In: Actes de la 6eme Rencontre Franco-Belge de Statisticiens, Bruxelles 1985. (1985) 
  13. X. Guyon, H. R. Künsch, Asymptotic comparison of estimators in the Ising model, In: Stochastic Models, Statistical Methods, and Algorithms in Image Analysis (P. Barone, A. Frigessi and M. Piccioni, eds., Lecture Notes in Statistics 74), Springer, Berlin 1992, pp. 177-198. (1992) MR1188486
  14. J. Hájek, Local asymptotic minimax and admissibility in estimation, In: Proc. 6th Berkeley Symposium, Vol. 1, Berkeley, Calif. 1970, pp. 175-194. (1970) MR0400513
  15. F. R. Hampel E. M. Ronchetti P. J. Rousseeuw, W. A. Stahel, Robust Statistics -- The Approach Based on Influence Functions, Wiley, New York 1986. (1986) MR0829458
  16. M. Janžura, Estimating interactions in binary lattice data with nearest-neighbor property, Kybernetika 23 (1987), 2, 136-142. (1987) MR0886826
  17. M. Janžura, Statistical analysis of Gibbs random fields, In: Trans. 10th Prague Conf. on Inform. Theory, Stat. Dec. Functions, Random Processes 1986, Praha, pp. 429-438. (1986) MR1136301
  18. M. Janžura, Asymptotic theory of parameter estimation for Gauss-Markov random fields, Kybernetika 24 (1988), 161-176. (1988) MR0953686
  19. M. Janžura, Local asymptotic normality for Gibbs random fields, In: Proceedings of the Fourth Prague Symposium on Asymptotic Statistics (P. Mandl, M. Hušková, eds.), Charles University, Prague 1989, pp. 275-284. (1989) MR1051446
  20. M. Janžura, P. Lachout, A central limit theorem for stationary random fields, Math. Methods Statist. 4 (1995), 463-472. (1995) MR1372017
  21. H. R. Künsch, Thermodynamics and statistical analysis of Gaussian random fields, Z. Wahrsch. Verw. Gebiete 58 (1981), 407-421. (1981) MR0639149
  22. H. Künsch, Decay of correlations under Dobrushin's uniqueness condition and its applications, Commun. Math. Phys. 84 (1982), 207-222. (1982) Zbl0495.60097MR0661133
  23. H. Künsch, Infinitesimal robustness for autoregressive processes, Ann. Statist. 12 (1984), 843-863. (1984) MR0751277
  24. C. Preston, Random Fields, (Lecture Notes in Mathematics 534). Springer, Berlin 1976. (1976) Zbl0335.60074MR0448630
  25. D. J. Strauss, Analysing binary lattice data with the nearest-neighbor property, J. Appl. Probab. 12 (1975), 702-712. (1975) Zbl0322.62072MR0386122
  26. L. Younès, Estimation and annealing for Gibbsian fields, Ann. Inst. H. Poincaré Sect. B (N. S.) 24 (1988), 269-294. (1988) MR0953120
  27. L. Younès, Parametric inference for imperfectly observed Gibbsian fields, Probab. Theory Related Fields 82 (1989), 625-645. (1989) MR1002904

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