# International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

# Estimation Problems for Random Fields

• Mikhail P. Moklyachuk
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-04898-2_236

Estimation problems for random fields X (t),   t ∈ ℝ n (estimation of the unknown mathematical expectation, estimation of the correlationfunction, estimation of regression parameters, extrapolation, interpolation, filtering,etc) are similar to the corresponding problems for (random fields of dimension 1). Complications usually are caused by the form of domain of points {tj} = D ⊂ ℝ n, where observations {X (tj) } are given, and by the dimension of the field. The complications can be overcome by considering specific domains of observations and particular classes of random fields.

Say in the domain D ⊂ ℝ n there are given observations of the random field
$$X\left (t\right ) = \sum \limits_{i=1}^{q}\theta,{g}_{ i}(t) + Y (t),$$
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