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Mathematics > Statistics Theory

arXiv:0707.1384 (math)
[Submitted on 10 Jul 2007]

Title:Asymptotically Optimal Estimator of the Parameter of Semi-Linear Autoregression

Authors:Dmytro Ivanenko
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Abstract: The difference equations $\xi_{k}=af(\xi_{k-1})+\epsilon_{k}$, where $(\epsilon_k)$ is a square integrable difference martingale, and the differential equation ${\rm d}\xi=-af(\xi){\rm d}t+{\rm d}\eta$, 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.
Comments: 10 pages
Subjects: Statistics Theory (math.ST); Dynamical Systems (math.DS); Applications (stat.AP)
MSC classes: 62F12; 60F05
Cite as: arXiv:0707.1384 [math.ST]
  (or arXiv:0707.1384v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.0707.1384

Submission history

From: Dmitry Ivanenko Alexandrovich [view email]
[v1] Tue, 10 Jul 2007 08:48:06 UTC (8 KB)
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