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ON ESTIMATION OF FUNCTIONS OF A PARAMETER OBSERVED IN GAUSSIAN NOISE

ON ESTIMATION OF FUNCTIONS OF A PARAMETER OBSERVED IN GAUSSIAN NOISE

Authors :
Ibragimov, I.A.
Source :
Journal of Mathematical Sciences. April 9, 2019, Vol. 238 Issue 4, p463, 8 p.
Publication Year :
2019

Abstract

The main problem of the paper looks as follows. A functional parameter [theta] [member of] [THETA] [subset] [L.sub.2](- -[infinity], [infinity]) is observed in Gaussian noise. The problem is to estimate the value F([theta]) of a given function F. A construction of asymptotically efficient estimates for F([theta]) is suggested under the condition that [THETA] admits approximations by subspaces [H.sub.T] [subset] [L.sub.2] with reproducing kernels [K.sub.T](t, s), [K.sub.T](t, t) [less than or equal to] T. Bibliography: 10 titles.<br />1. Introduction. Main result 1.1. Consider the following general problem of statistical estimation. We have a statistical experiment {X, [??], {[P.sub.[theta]], [theta] [member of] [THETA]}} generated by an observation [X.sub.[epsilon]] [...]

Subjects

Subjects :
Bibliographies
Mathematics

Details

Language :
English
ISSN :
10723374
Volume :
238
Issue :
4
Database :
Gale General OneFile
Journal :
Journal of Mathematical Sciences
Publication Type :
Academic Journal
Accession number :
edsgcl.598930143
Full Text :
https://doi.org/10.1007/s10958-019-04250-9