Geodesic
A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 289-299 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the paper, we construct the lower and upper bounds of the minimax risk in the estimation problem, as we observe the unknoun pseudo periodic function in stationary noise with a density satisfying the local version of the Muckenhoupt condition. 
@article{ZNSL_2017_466_a18,
     author = {V. N. Solev},
     title = {A local version of the {Muckenhoupt} condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {289--299},
     year = {2017},
     volume = {466},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a18/}
}
TY  - JOUR
AU  - V. N. Solev
TI  - A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 289
EP  - 299
VL  - 466
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a18/
LA  - ru
ID  - ZNSL_2017_466_a18
ER  - 
%0 Journal Article
%A V. N. Solev
%T A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 289-299
%V 466
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a18/
%G ru
%F ZNSL_2017_466_a18
V. N. Solev. A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 289-299. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a18/

[1] Yu. A. Rozanov, Statsionarnye protsessy, Mir, M., 1963 | MR

[2] I. A. Ibragimov, Yu. A. Rozanov, Gaussovskie protsessy, Mir, M., 1974

[3] I. A. Ibragimov, R. Z. Khasminskii, “O neparametricheskom otsenivanii znacheniya lineinogo funktsionala v gaussovskom belom shume”, Teoriya veroyatn. i ee primen., 29:1 (1984), 19–32 | MR | Zbl

[4] W. Stepanoff, “Sur quelques generalisations des fonctions presque-periodiques”, Comptes Rendus, 181 (1925), 90–92 | Zbl

[5] N. Viner, R. Peli, Preobrazovanie Fure v kompleksnoi ploskosti, Nauka, M., 1964 | MR

[6] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981 | MR | Zbl

[7] S. V. Reshetov, “Minimaksnaya otsenka psevdo-periodicheskoi funktsii, nablyudaemoi na fone statsionarnogo shuma”, Vestnik SPbGU. Seriya 1, 2 (2010), 106–115

[8] V. N. Solev, “Uslovie lokalnoi asimptoticheskoi normalnosti dlya gaussovskikh statsionarnykh protsessov”, Zap. nauchn. semin. POMI, 278, 2001, 225–247 | MR | Zbl

[9] V. N. Solev, “Adaptivnaya otsenka funktsii, nablyudaemoi na fone gaussovskogo statsionarnogo shuma”, Zap. nauchn. semin. POMI, 454, 2016, 261–275 | MR