Asymptotically Optimal Estimator of the Parameter of Semi-Linear Autoregression

Details Asymptotically Optimal Estimator of the Parameter of Semi-Linear Autoregression Asymptotically Optimal Estimator of the Parameter of Semi-Linear Autoregression

2007-07-10

arxiv.org/abs/0707.1384v1

Mathematics

Statistics Theory

10 pages

Scientific paper

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.

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