Geodesic
Asymptotically optimal estimator of
Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 77-85

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The difference equations $\xi_k=af(\xi_{k-1})+\varepsilon_k,$ where$\varepsilon_k$ is a square integrable difference martingale, and the differential equation $d\xi=-af(\xi)dt+d\eta,$ 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.
Keywords: estimator, optimization
Mots-clés : Martingale, convergence. 
@article{THSP_2007_13_1_a7,
     author = {Dmytro Ivanenko},
     title = {Asymptotically optimal estimator of},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {77--85},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a7/}
}
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Dmytro Ivanenko. Asymptotically optimal estimator of. Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 77-85. http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a7/