Konev, V.; Pergamenshchikov, S. Sequential estimation of the parameters in a trigonometric regression model with the Gaussian coloured noise. (English) Zbl 1031.62062 Stat. Inference Stoch. Process. 6, No. 3, 215-235 (2003). 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. Cited in 10 Documents 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 Keywords:fixed-accuracy estimation; periodic regression; coloured noise; nuisance parameter PDFBibTeX XMLCite \textit{V. Konev} and \textit{S. Pergamenshchikov}, Stat. Inference Stoch. Process. 6, No. 3, 215--235 (2003; Zbl 1031.62062) Full Text: DOI