### ASYMPTOTICALLY OPTIMAL ESTIMATOR OF THE PARAMETER OF SEMI-LINEAR AUTOREGRESSION

**DMYTRO IVANENKO**

*Theory of Stochastic Processes*

*Vol.13 (29), no.1-2, 2007, pp.77-85*

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