Geodesic
Truncated estimation method and applications
Serdica Mathematical Journal, Tome 43 (2017) no. 3-4, pp. 221-266

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This paper presents an estimation method of ratio type functionals by dependent sample of fixed size. This method makes it possible to obtain estimators with guaranteed accuracy in the sense of the L2m-norm, m ≥ 1. As an illustration, some parametric estimation problems on a time interval of a fixed length are considered. In particular, parameters of linear continuous-time and non-linear discrete-time processes are estimated. Moreover, the parameter estimation problem of non-Gaussian Ornstein– Uhlenbeck process by discrete-time observations with guaranteed accuracy is solved. In addition to non-asymptotic properties, the limit behavior of presented estimators is investigated. It is shown that all the truncated estimators have rates of convergence of the estimators they are based upon. These estimators are used for the construction of adaptive predictors for dynamical systems with unknown parameters.
Keywords: Adaptive optimal prediction, dynamic systems, autoregressive processes, stochastic differential equations, stochastic differential equations with time delay, risk function; guaranteed parameter estimation, 60G25, 62M20, 60G52, 60J60, 62F12, 93E10 
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     title = {Truncated estimation method and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2017_43_3-4_a1/}
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Dogadova, Tatiana V.; Kusainov, Marat I.; Vasiliev Vyacheslav A. Truncated estimation method and applications. Serdica Mathematical Journal, Tome 43 (2017) no. 3-4, pp. 221-266. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_3-4_a1/