On Estimation of Functions of a Parameter Observed in Gaussian Noise

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 admit...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2019-04, Vol.238 (4), p.463-470
Main Author: Ibragimov, I. A.
Format: Article
Language:English
Subjects:
Bibliographies
Mathematics
Mathematics and Statistics
Noise control
Normal distribution
Parameter estimation
Random noise
Subspaces
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Summary: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 .
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04250-9