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Almost sure central limit theorems for random ratios and applications to LSE for fractional Ornstein-Uhlenbeck processes

Cénac P., Es-Sebaiy K.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 2

285--300

We will investigate an almost sure central limit theorem (ASCLT) for sequences of random variables having the form of a ratio of two terms such that the numerator satisfies the ASCLT and the denominator is a positive term which converges almost surely to one. This result leads to the ASCLT for least squares estimators for Ornstein-Uhlenbeck proces driven by fractional Brownian motion.

On-line parameter and delay estimation of continuous-time dynamic systems

Kozłowski J., Kowalczuk Z.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 2

223--232

The problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous identification of input delay and spectral parameters of the system models. The performance of the proposed estimation algorithms is verified in an illustrative numerical simulation study.

An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

Bian J., Peng H., Xing J., Liu Z., Li H.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 1

117--129

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton–Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton–Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.