Asymptotically optimal estimator of the parameter of semi-linear autoregression

Dmytro Ivanenko

Department of Mathematics and Theoretical Radiophysic, Kyiv National Taras Shevchenko University, Kyiv, Ukraine

Abstract: The difference equations $\xi_k=af(\xi_{k-1})+\varepsilon_k,$ where$\varepsilon_k$ is a square integrable difference martingale, and the differential equation $d\xi=-af(\xi)dt+d\eta,$ where $\eta$ 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.

Keywords: Martingale, estimator, optimization, convergence.

MSC: Primary 62F12; Secondary 60F05

Language: English

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