Convergence of estimates for partitions in the disorder problem for random fields. (English. Russian original) Zbl 0834.62097

Kaplan, E. I.

Theory Probab. Math. Stat. 47, 35-39 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 34-39 (1992).

Summary: The problem of a posteriori estimation of homogeneous domains in random fields is investigated. Conditions for consistency and the asymptotic order convergence of the estimates are studied. The relationship between the limit behavior of the estimates, the ergodic properties of an observed field and the geometric structure of homogeneous domains is analyzed.

MSC:

62M40	Random fields; image analysis
62G20	Asymptotic properties of nonparametric inference

Keywords:

a posteriori estimation of homogeneous domains; consistency; asymptotic order convergence; ergodic properties; geometric structure