Asymptotic results in parameter estimation for Gibbs random fields
Kybernetika (1997)
- Volume: 33, Issue: 2, page 135-159
- ISSN: 0023-5954
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topJanžura, Martin. "Asymptotic results in parameter estimation for Gibbs random fields." Kybernetika 33.2 (1997): 135-159. <http://eudml.org/doc/27456>.
@article{Janžura1997,
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 = {http://eudml.org/doc/27456},
volume = {33},
year = {1997},
}
TY - JOUR
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 - http://eudml.org/doc/27456
ER -
References
top- J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. B 36 (1974), 192-226. (1974) Zbl0327.60067MR0373208
- J. Besag, On the statistical analysis of dirty pictures (with discussion), J. Roy. Statist. Soc. Ser. B 48 (1986), 259-302. (1986) Zbl0609.62150MR0876840
- E. Bolthausen, On the central limit theorem for stationary mixing random fields, Ann. Probab. 10 (1982), 1047-1050. (1982) Zbl0496.60020MR0672305
- 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
- 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
- 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)
- 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
- H. O. Georgii, Gibbs Measures and Phase Transitions, De Gruyter, Berlin 1988. (1988) Zbl0657.60122MR0956646
- 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
- 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)
- L. Gross, Absence of second-order phase transition in the Dobrushin's uniqueness region, J. Statist. Phys. 27 (1981), 57-72. (1981) MR0610692
- 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)
- 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
- J. Hájek, Local asymptotic minimax and admissibility in estimation, In: Proc. 6th Berkeley Symposium, Vol. 1, Berkeley, Calif. 1970, pp. 175-194. (1970) MR0400513
- 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
- M. Janžura, Estimating interactions in binary lattice data with nearest-neighbor property, Kybernetika 23 (1987), 2, 136-142. (1987) MR0886826
- 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
- M. Janžura, Asymptotic theory of parameter estimation for Gauss-Markov random fields, Kybernetika 24 (1988), 161-176. (1988) MR0953686
- 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
- M. Janžura, P. Lachout, A central limit theorem for stationary random fields, Math. Methods Statist. 4 (1995), 463-472. (1995) MR1372017
- H. R. Künsch, Thermodynamics and statistical analysis of Gaussian random fields, Z. Wahrsch. Verw. Gebiete 58 (1981), 407-421. (1981) MR0639149
- H. Künsch, Decay of correlations under Dobrushin's uniqueness condition and its applications, Commun. Math. Phys. 84 (1982), 207-222. (1982) Zbl0495.60097MR0661133
- H. Künsch, Infinitesimal robustness for autoregressive processes, Ann. Statist. 12 (1984), 843-863. (1984) MR0751277
- C. Preston, Random Fields, (Lecture Notes in Mathematics 534). Springer, Berlin 1976. (1976) Zbl0335.60074MR0448630
- D. J. Strauss, Analysing binary lattice data with the nearest-neighbor property, J. Appl. Probab. 12 (1975), 702-712. (1975) Zbl0322.62072MR0386122
- L. Younès, Estimation and annealing for Gibbsian fields, Ann. Inst. H. Poincaré Sect. B (N. S.) 24 (1988), 269-294. (1988) MR0953120
- L. Younès, Parametric inference for imperfectly observed Gibbsian fields, Probab. Theory Related Fields 82 (1989), 625-645. (1989) MR1002904
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