Reducing the bias of the wavelet estimate of spectral density
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2013), pp. 27-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is devoted to the development of methods of the bias reduction for a wavelet estimate of spectral density of a stationary discrete time random process. The method is based on an estimate for the upper boundary of the bias obtained limited spectral densities satisfying the Lipschitz condition. These results can be used for creating algorithms for the calculation of wavelet estimates of spectral densities with a given accuracy.
Keywords: wavelet estimate bias, spectral density, stationary random process.
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N. V. Semenchuk. Reducing the bias of the wavelet estimate of spectral density. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2013), pp. 27-36. http://geodesic.mathdoc.fr/item/VTGU_2013_6_a3/

[1] Neumann M. H., “Spectral density estimation via nonlinear wavelet methods for stationary non-Gaussian time series”, J. Time Ser. Anal., 17:6 (1996), 137–166 | DOI | MR

[2] Dobeshi I., Desyat lektsii po veivletam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001, 464 pp.

[3] Brillindzher D., Vremennye ryady. Obrabotka dannykh i teoriya, Mir, M., 1980, 560 pp. | MR

[4] Semenchuk N. V., Trush N. N., “Skorost skhodimosti momentov otsenki spektralnoi plotnosti, postroennoi pri pomoschi veivletov”, Obozrenie prikladnoi i promyshlennoi matematiki, 16:5 (2009), 761–771

[5] Trush N. N., Asimptoticheskie metody statisticheskogo analiza vremennykh ryadov, BGU, Minsk, 1999, 218 pp.

[6] Terpugov A. F., Matematicheskaya statistika, Izd-vo Tom. un-ta, Tomsk, 1974, 138 pp.

[7] Kendall M., Styuart A., Teoriya raspredelenii, Mir, M., 1966, 588 pp.

[8] Quenoulee M. H., “Notes on bias in estimation”, Biometrica, 43 (1956), 353–359 | DOI | MR

[9] Semenchuk N. V., Trush N. N., “Skorost skhodimosti smescheniya otsenki spektralnoi plotnosti, postroennoi s pomoschyu masshtabiruyuschei funktsii Koifmana”, Vestn. Belorus. un-ta. Ser. 1, 2009, no. 2, 57–61 | MR