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arXiv · 0707.1384

Asymptotically Optimal Estimator of the Parameter of Semi-Linear Autoregression

Dmytro Ivanenko
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Abstract

The difference equations $ξ_{k}=af(ξ_{k-1})+ε_{k}$, where $(ε_k)$ is a square integrable difference martingale, and the differential equation ${\rm d}ξ=-af(ξ){\rm d}t+{\rm d}η$, 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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Dmytro Ivanenko. 2007-07-10. Asymptotically Optimal Estimator of the Parameter of Semi-Linear Autoregression. https://arxiv.org/abs/0707.1384

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