Geodesic
The lower bound of the minimax risk in a problem of estimating the function in stationary gaussian noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 282-293 
V. N. Solev. The lower bound of the minimax risk in a problem of estimating the function in stationary gaussian noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 31, Tome 505 (2021), pp. 282-293. http://geodesic.mathdoc.fr/item/ZNSL_2021_505_a15/
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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 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 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] D. L. Donoho, R. C. Liu, B. MacGibbon, “Minimax risk over hyperrectangles, and implications”, The Ann. Statist., 18:3 (1990), 1416–1437 | DOI | 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] B. J. Garnett, Bounded Analytic Functions, Academic Press, N.Y., 1981 | 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] V. N. Solev, “Otsenka funktsii v gaussovskom statsionarnom shume”, Zap. nauchn. semin. POMI, 495, 2020, 277–290 | MR

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

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