MATHEMATICS

On sequential estimation of a periodic signal on the background of an autoregressive noise

T. V. Emelyanova, V. V. Konev

Tomsk State University, Tomsk, Russian Federation

Abstract: 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, autoregressive noise.

UDC: 519.216.3

Received: 11.02.2015

DOI: 10.17223/19988621/34/2

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