Estimation of function observed in stationary noise: discretization
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 286-298 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the article we propose a new estimation of the unknown pseudo periodic function which observed in stationary noise. We compare the accuracy of the proposed estimation with the minimax risk.
@article{ZNSL_2015_441_a17,
     author = {V. N. Solev},
     title = {Estimation of function observed in stationary noise: discretization},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {286--298},
     year = {2015},
     volume = {441},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a17/}
}
TY  - JOUR
AU  - V. N. Solev
TI  - Estimation of function observed in stationary noise: discretization
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 286
EP  - 298
VL  - 441
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a17/
LA  - ru
ID  - ZNSL_2015_441_a17
ER  - 
%0 Journal Article
%A V. N. Solev
%T Estimation of function observed in stationary noise: discretization
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 286-298
%V 441
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a17/
%G ru
%F ZNSL_2015_441_a17
V. N. Solev. Estimation of function observed in stationary noise: discretization. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 286-298. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a17/

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

[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 primenen., 29:1 (1984), 19–32 | MR | Zbl

[4] D. L. Donoho, R. C. Liu, B. MacGibbon, “Minimax risk over hyperrectangles, and implications”, Ann. Statist., 18:3 (1990), 1416–1437 | DOI | MR | Zbl

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

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

[7] J. B. Garnett, Bounded Analytic Functions, Academic Press, NY, 1981 | MR | Zbl

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

[9] S. V. Reshetov, “Minimaksnaya otsenka psevdo-periodicheskoi funktsii, nablyudaemoi na fone statsionarnogo shuma”, Vestnik SPbGU, Ser. 1. Matem., Mekhan., Astron., 2010, no. 2, 106–115 | MR