Estimation of Mathematical Expectation

Abstract

Consider the random field

$$ \xi (x)\, = \,\xi _\theta (x)\, = \,g(x,\theta )\, + \,\varepsilon (x), $$

(3.1.1)

where g(x, θ) : R ⁿ × Ө^c → R ¹ is a function depending on an unknown parameter θ ∈ Ө ∈ B ^q and ε (x), x ∈ R ⁿ, is a random field with zero mean. Assume that in R ⁿ a system of measurable bounded sets m = {Δ} is selected and Δ → ∞. The problem is to estimate the parameter θ from observations of the random field ξ(x) on the sets Δ → ∞.