Asymptotically optimal estimator of the parameter of semi-linear autoregression
The difference equations ξk = af(ξk-1) + εk, where (εk) is a square integrable difference martingale, and the differential equation dξ =-af(ξ)dt + dη, where η is a square integrable martingale, are considered. A family of estimators depending, besides the sample size n (or the observation period, if...
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| Date: | 2007 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/4475 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Asymptotically optimal estimator of the parameter of semi-linear autoregression / D. Ivanenko // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 1-2. — С.77-85. — Бібліогр.: 7 назв.— англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The difference equations ξk = af(ξk-1) + εk, where (εk) is a square integrable difference martingale, and the differential equation dξ =-af(ξ)dt + dη, where η is a square integrable martingale, are considered. A family of estimators depending, besides the sample size n (or the observation period, if time is continuous) on some random Lipschitz functions is constructed. Asymptotic optimality of this estimators is investigated. |
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