Title :
On identification of linear dynamic systems with an unknown distribution of the noises
Author :
Koshkin, G.M. ; Vasil´ev, V.A.
Author_Institution :
Dept. of Appl. Math. & Cybern., Tomsk State Univ., Russia
Abstract :
The problem of construction of the probabilistic models for dynamic systems with unknown noise distribution is considered. The proposed approach is based on the construction of one-step predictors and estimators for the limiting probability density for the sequence of forecast errors. The estimates for this probability density and its derivatives with improved convergence rate in mean square sense are given and studied. This forecasting method is applied to linear dynamic systems. In this case the presence of the dependence in the sequence of forecast errors doesn´t influence asymptotical properties of estimates of the probability density and its derivatives. The convergence with probability 1 and uniform asymptotic normality of estimates are proved. The estimation problems of the limiting probability density have been solved also in the case of the martingale difference noise both for the deterministic and stochastic regression processes
Keywords :
convergence; forecasting theory; identification; noise; probability; asymptotical properties; deterministic regression processes; forecast error sequence; identification; limiting probability density; linear dynamic systems; martingale difference noise; mean square convergence; one-step estimators; one-step predictors; probabilistic models; probability density; stochastic regression processes; uniform asymptotic normality; unknown noise distribution; Convergence; Cybernetics; Kernel; Mathematics; Parametric statistics; Predictive models; Probability density function; Random variables; Statistical analysis; Stochastic resonance;
Conference_Titel :
Decision and Control, 1996., Proceedings of the 35th IEEE Conference on
Conference_Location :
Kobe
Print_ISBN :
0-7803-3590-2
DOI :
10.1109/CDC.1996.577387
