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Sequential estimation of the parameters in a trigonometric regression model with the Gaussian coloured noise. (English) Zbl 1031.62062

Summary: This paper considers the estimation problem for a trigonometric regression model with the noise specified by the Ornstein-Uhlenbeck process with unknown parameter. We propose a sequential procedure which ensures a prescribed mean square precision uniformly in the nuisance parameter. The asymptotic behaviour of the procedure duration mean has been studied.

MSC:

62L12 Sequential estimation
62M05 Markov processes: estimation; hidden Markov models
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
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