Geodesic
Estimation of a vector valued function in a Gaussian stationary noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 275-285 
V. N. Solev. Estimation of a vector valued function in a Gaussian stationary noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 275-285. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a17/
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     author = {V. N. Solev},
     title = {Estimation of a vector valued function in a {Gaussian} stationary noise},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a17/}
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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 bound of the minimax risk in the estimation problem, as we observe the unknoun pseudo-periodic vector-function in a Gaussian stationary noise with the spectral density satisfying the vector 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, Liu Richard C., MacGibbon Brenda, “Minimax Risk over Hyperrectangles, and Implications”, Ann. Statist., 18:3, 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] J. B. Garnett, Bounded analytic functions, Academic Press, NY, 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] S. V. Reshetov, “Minimaksnyi risk dlya kvadratichno vypuklykh mnozhestv”, Zap. nauchn. semin. POMI, 368, 2009, 181–189

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

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

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

[12] 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

[13] V. N. Solev, “Uslovie Makkenkhaupta i odna zadacha otsenivaniya”, Zap. nauchn. semin. POMI, 431, 2014, 186–197

[14] S. R. Treil, A. L. Volberg, “Weighted embeddings and weighted norm inequalities for the Hilbert transform and the maximal operator”, Algebra i analiz, 7:6 (1995), 205–226 | MR