zbMATH — the first resource for mathematics

Test for submodel in Gibbs-Markov binary random sequence. (English) Zbl 0674.60094
Summary: The Gibbs-Markov random sequences (as studied in frame of statistical physics) are convenient as probability models for sequences of dependent binary data. Thus, the model is given by a system of interactions which may be understood and estimated as a vector parameter. Setting some of the interactions equal to zero, we obtain a submodel. A test for the submodel is derived in the present paper, and a numerical example with simulated data is included.
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B05 Classical equilibrium statistical mechanics (general)
60J99 Markov processes
Full Text: Link EuDML
[1] Y. M. M. Bishop S. E. Fienberg, P. W. Holland: Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge, Mass. 1975. · Zbl 0332.62039
[2] R. L. Dobrushin: Conditions of absence of phase transitions for one-dimensional classical model. Mat. Sbornik 93 (1974), 29-49. In Russian.
[3] R. L. Dobrushin, B. S. Nahapetian: Strong convexity of the pressure for lattice systems of classical statistical physics. Teoret. Mat. Fiz. 20 (1974), 223-234. In Russian. · Zbl 0311.60063
[4] I. Ekeland, R. Temam: Convex Analysis and Variational Problems. North-Holland, Amsterdam 1976. · Zbl 0322.90046
[5] M. Janžura: Estimating interactions in binary data sequences. Kybernetika 22 (1986), 277-284. · Zbl 0629.60104
[6] M. Janžura: Estimating interactions in binary lattice data with nearest-neighbor property. Kybernetika 23 (1987), 136-142. · Zbl 0668.62059 · eudml:28026
[7] H. Künsch: Decay of correlations under Dobrushin’s uniqueness condition and its applications. Commun. Math. Phys. 84 (1982), 207-222. · Zbl 0495.60097 · doi:10.1007/BF01208568
[8] C. Preston: Random Fields. Lecture Notes in Mathematics 534. Springer-Verlag, Berlin–Heidelberg–New York 1976. · Zbl 0335.60074 · doi:10.1007/BFb0080563
[9] C. R. Rao: Linear Statistical Inference and its Applications. John Wiley and Sons, New York 1973. · Zbl 0256.62002
[10] D. Ruelle: Statistical Mechanics. Rigorous Results. Benjamin, New York 1969. · Zbl 0177.57301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.