ASYMPTOTICALLY OPTIMAL ESTIMATOR OF THE PARAMETER OF SEMI-LINEAR AUTOREGRESSION
DMYTRO IVANENKOTheory 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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