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Title: Asymptotic results in parameter estimation for Gibbs random fields (English)
Author: Janžura, Martin
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 33
Issue: 2
Year: 1997
Pages: 135-159
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Category: math
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MSC: 62F12
MSC: 62M40
MSC: 93E10
idZBL: Zbl 0962.62092
idMR: MR1454275
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Date available: 2009-09-24T19:07:46Z
Last updated: 2012-06-06
Stable URL: http://hdl.handle.net/10338.dmlcz/124301
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Reference: [1] J. Besag: Spatial interaction and the statistical analysis of lattice systems.J. Roy. Statist. Soc. B 36 (1974), 192-226. Zbl 0327.60067, MR 0373208
Reference: [2] J. Besag: On the statistical analysis of dirty pictures (with discussion).J. Roy. Statist. Soc. Ser. B 48 (1986), 259-302. Zbl 0609.62150, MR 0876840
Reference: [3] E. Bolthausen: On the central limit theorem for stationary mixing random fields.Ann. Probab. 10 (1982), 1047-1050. Zbl 0496.60020, MR 0672305
Reference: [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. MR 1150354
Reference: [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. MR 0468967
Reference: [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.
Reference: [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. Zbl 0665.68067, MR 0934354
Reference: [8] H. O. Georgii: Gibbs Measures and Phase Transitions.De Gruyter, Berlin 1988. Zbl 0657.60122, MR 0956646
Reference: [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. MR 0934721
Reference: [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.
Reference: [11] L. Gross: Absence of second-order phase transition in the Dobrushin's uniqueness region.J. Statist. Phys. 27 (1981), 57-72. MR 0610692
Reference: [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.
Reference: [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. MR 1188486
Reference: [14] J. Hájek: Local asymptotic minimax and admissibility in estimation.In: Proc. 6th Berkeley Symposium, Vol. 1, Berkeley, Calif. 1970, pp. 175-194. MR 0400513
Reference: [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. MR 0829458
Reference: [16] M. Janžura: Estimating interactions in binary lattice data with nearest-neighbor property.Kybernetika 23 (1987), 2, 136-142. MR 0886826
Reference: [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. MR 1136301
Reference: [18] M. Janžura: Asymptotic theory of parameter estimation for Gauss-Markov random fields.Kybernetika 24 (1988), 161-176. MR 0953686
Reference: [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. MR 1051446
Reference: [20] M. Janžura, P. Lachout: A central limit theorem for stationary random fields.Math. Methods Statist. 4 (1995), 463-472. MR 1372017
Reference: [21] H. R. Künsch: Thermodynamics and statistical analysis of Gaussian random fields.Z. Wahrsch. Verw. Gebiete 58 (1981), 407-421. MR 0639149
Reference: [22] H. Künsch: Decay of correlations under Dobrushin's uniqueness condition and its applications.Commun. Math. Phys. 84 (1982), 207-222. Zbl 0495.60097, MR 0661133
Reference: [23] H. Künsch: Infinitesimal robustness for autoregressive processes.Ann. Statist. 12 (1984), 843-863. MR 0751277
Reference: [24] C. Preston: Random Fields.(Lecture Notes in Mathematics 534). Springer, Berlin 1976. Zbl 0335.60074, MR 0448630
Reference: [25] D. J. Strauss: Analysing binary lattice data with the nearest-neighbor property.J. Appl. Probab. 12 (1975), 702-712. Zbl 0322.62072, MR 0386122
Reference: [26] L. Younès: Estimation and annealing for Gibbsian fields.Ann. Inst. H. Poincaré Sect. B (N. S.) 24 (1988), 269-294. MR 0953120
Reference: [27] L. Younès: Parametric inference for imperfectly observed Gibbsian fields.Probab. Theory Related Fields 82 (1989), 625-645. MR 1002904
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