Estimation of a function in a Gaussian stationary noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 277-290
V. N. Solev. Estimation of a function in a Gaussian stationary noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 277-290. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a16/
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     title = {Estimation of a function in a {Gaussian} stationary noise},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_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 upper bounds of the minimax risk in the estimation problem, as we observe the unknoun pseudo periodic function in a Gaussian stationary noise with the spectral density satisfying some local version of the Muckenhoupt condition.

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

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

[3] Donoho David L., Liu Richard C., MacGibbon Brenda, “Minimax Risk Over Hyperrectangles, and Implications”, The Ann. Stat., 18:3, 1416–1437 | 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

[6] Garnett, B. John, Bounded analytic functions, Academic Press, N-Y, 1981 | MR | Zbl

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

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

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

[10] 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

[11] V. N. Solev, “Otsenka funktsii v gaussovskom statsionarnom shume: novye spektralnye usloviya”, Zap. nauchn. semin. POMI, 486, 2018, 275–285

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

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