“…Let the function ψ be bounded, the distribution density of t ε on 1 R be nonnegative with 3 0 1 Eε = and 4 1 Eε < ∞ . In this case, the process (1) is the geometric Markov chain with the strong mixing coefficient [3][4][5] …”
To identify an unknown function defining of a nonlinear ARX-process, we use kernel regression estimators. The principal parts of mean square errors for these estimators are found. The proposed algorithms are applied to the real data processing.
“…Let the function ψ be bounded, the distribution density of t ε on 1 R be nonnegative with 3 0 1 Eε = and 4 1 Eε < ∞ . In this case, the process (1) is the geometric Markov chain with the strong mixing coefficient [3][4][5] …”
To identify an unknown function defining of a nonlinear ARX-process, we use kernel regression estimators. The principal parts of mean square errors for these estimators are found. The proposed algorithms are applied to the real data processing.
“…The recursive kernel estimators of the density function was introduced first by Wolverton and Wagner [20] and by Yamato independently [21] and examined thoroughly in [22]. The recursive kernel estimators of functionals of a multidimensional density function for strong mixing observations were studied in [23].…”
The structure of the estimators is similar to the recursive kernel estimators of a density function and its derivative. The estimators have been constructed using a single realization of Poisson process on a fixed time interval. Mean-square convergence has been proved in a scheme of series. Simulation studies have been carried out to illustrate the convergence.
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