Minimax estimations for functionals of random fields. (Russian) Zbl 0577.60051

Moklyachuk, M. P.

Teor. Veroyatn. Mat. Stat. 29, 84-92 (1983).

Let \(\xi =\xi (g,j)\) be a homogeneous random field on the product of a commutative locally compact topological group G with Z and values in a Hilbert space. The maximum error for linear estimation of the functional \[ A\xi =\int_{G}\sum^{\infty}_{j=0}<\xi (g,j),\quad a(g,j)>dg \] where \(\xi\) is observed on the set \(\{\) (g,j): \(g\in G\), \(j=-1,-2,...\}\) and the function a fulfills certain boundedness conditions, is given.
Furthermore the field \(\xi_ o\), which gives the maximum error, is explicitly determined.

Reviewer: C.Baldauf

MSC:

60G60	Random fields
60B15	Probability measures on groups or semigroups, Fourier transforms, factorization
62M09	Non-Markovian processes: estimation

Keywords:

homogeneous random field; compact topological group; linear estimation