Estimation of function in Gaussian stationary noise: new spectral condition
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 222-232
V. N. Solev. Estimation of function in Gaussian stationary noise: new spectral condition. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 222-232. http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a16/
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     author = {V. N. Solev},
     title = {Estimation of function in {Gaussian} stationary noise: new spectral condition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {222--232},
     year = {2018},
     volume = {474},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a16/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 the spectral density satisfying the new spectral condition.

[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 | 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

[7] J. B. Garnett, Bounded analytic functions, Academic Press, New York, 1981 | MR | Zbl

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

[9] S. V. Reshetov, “Minimaksnyi risk dlya kvadratichno vypuklykh mnozhestv”, Zap. nauchn. semin. POMI, 368, 2009, 181–189

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

[11] V. N. Solev, “Otsenka funktsii, nablyudaemoi na fone statsionarnogo shuma: diskretizatsiya”, Zap. nauchn. semin. POMI, 441, 2015, 286–298

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

[13] V. N. Solev, “Lokalnaya versiya usloviya Makkenkhaupta i tochnost otsenivaniya neizvestnoi psevdo-periodicheskoi funktsii, nablyudaemoi na fone statsionarnogo shuma”, Zap. nauchn. semin. POMI, 466, 2017, 261–275