On minimax estimation of linear transforms of random fields with values in Hilbert space. (English. Russian original) Zbl 0634.60049

Tatarinov, S. V.; Moklyachuk, M. P.

Theory Probab. Math. Stat. 35, 127-136 (1987); translation from Teor. Veroyatn. Mat. Stat. 35, 111-118 (1986).

Let \(\xi\) (m,n) be a homogeneous random field defined on the integer lattice \(Z^ 2\) and with values in a Hilbert space. The problem of minimax estimation of a linear transform \[ A\xi =\sum^{\infty}_{m=0}\sum^{\infty}_{n=0}<\xi (m,n),a(m,n)> \] from observations of the field at the points of the set \(Z^ 2\setminus Z^ 2_+\) \((Z^ 2_+=\{(m,n):\) \(m\geq 0\), \(n\geq 0\}\) are considered.

Reviewer: M.Yadrenko

MSC:

60G60	Random fields
62G05	Nonparametric estimation

Keywords:

random field; minimax estimation of a linear transform