On sequential estimation of a periodic signal on the background of an autoregressive noise | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2015. № 2(34).

HomeIssuesOn sequential estimation of a periodic signal on the background of an autoregressive noise | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2015. № 2(34).

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

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.

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Keywords

последовательное оценивание, заданная среднеквадрати-ческая точность, тригонометрическая регрессия, момент остановки, авторегрессионный шум, sequential estimation, given root-mean-square accuracy, trigonometric regression, stopping time, autoregressive noise

Authors

NameOrganizationE-mail
Emelyanova Tatiana VeniaminovnaTomsk State Universitytv_em@mail.ru
Konev Viktor Vasil'evichTomsk State Universityvvkonev@mail.tsu.ru
Всего: 2

References

Андерсон Т. Статистический анализ временных рядов. М.: Мир, 1976.
Ибрагимов И.А., Хасьминский Р.З. Асимптотическая теория оценивания. М.: Наука, 1979.
Липцер Р.Ш., Ширяев А.Н. Статистика случайных процессов. М.: Наука, 1974.
Konev V., Pergamenshchikov S. On guaranteed estimation of the mean of an autoregressive process // Ann. Statist. 1997. V. 25. No. 5. P. 2127-2163.
Конев В.В., Пергаменщиков С.М. Гарантированное оценивание периодического сигнала на фоне авторегрессионных помех с неизвестными параметрами // Проблемы передачи информации. 1997. Т. 3. Вып. 4.
Galtchouk L., Konev V. On Sequential Least Squares Estimates of Autoregressive Parameters // Sequential Analysis. 2005. V. 24. No. 4. P. 335-364.
Ширяев А.Н. Вероятность. М.: Наука, 1989.
On sequential estimation of a periodic signal on the background of an autoregressive noise | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2015. № 2(34).

On sequential estimation of a periodic signal on the background of an autoregressive noise | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2015. № 2(34).

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