On Estimation of Functions of a Parameter Observed in Gaussian Noise

Abstract

The main problem of the paper looks as follows. A functional parameter θ ∈ Θ ⊂ L₂(−∞,∞) 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 ⊂ L₂ with reproducing kernels K_T (t, s), K_T (t, t) ≤ T.