Geodesic
On sequential estimation of a periodic signal on the background of an autoregressive noise
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2015), pp. 18-29

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We consider the problem of estimating coefficients of a trigonometric signal in a discrete time from observations with an additive noise described by a stationary autoregressive process with unknown parameters and unknown distribution. A one-step sequential procedure to estimate signal coefficients is proposed, which provides a given root-mean-square accuracy of estimates for any values of the nuisance parameters. An asymptotic formula for the mean duration of the procedure is constructed.
Keywords: sequential estimation, given root-mean-square accuracy, trigonometric regression, stopping time
Mots-clés : autoregressive noise. 
@article{VTGU_2015_2_a1,
     author = {T. V. Emelyanova and V. V. Konev},
     title = {On sequential estimation of a periodic signal on the background of an autoregressive noise},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {18--29},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2015_2_a1/}
}
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T. V. Emelyanova; V. V. Konev. On sequential estimation of a periodic signal on the background of an autoregressive noise. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2015), pp. 18-29. http://geodesic.mathdoc.fr/item/VTGU_2015_2_a1/