ON ESTIMATION OF FUNCTIONS OF A PARAMETER OBSERVED IN GAUSSIAN NOISE

摘要

The main problem of the paper looks as follows. A functional parameter θ ∈ Θ ⊂ L_2(-∞, ∞) is observed in Gaussian noise. The problem is to estimate the value F(θ) of a given function F. A construction of asymptotically efficient estimates for F(θ) is suggested under the condition that Θ admits approximations by subspaces H_T ⊂ L_2 with reproducing kernels K_T(t,s), K_T(t,t) ≤ T. Bibliography: 10 titles.