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On adaptive smoothing of empirical transfer function estimates

2000; Elsevier BV; Volume: 8; Issue: 11 Linguagem: Inglês

10.1016/s0967-0661(00)00065-4

1873-6939

Anders Stenman, Fredrik Gustafsson, Daniel E. Rivera, Lennart Ljung, Tomas McKelvey,

Statistical and numerical algorithms

The determination of the right resolution parameter when estimating frequency functions of linear systems is a trade-off between bias and variance. Traditional non-parametric approaches, like "window-closing" employ a global resolution parameter — the window width — that is tuned by ad hoc methods, usually visual inspection of the results. This paper suggests a method that tunes such parameters by an automatic procedure. A further benefit is that the tuning can be performed locally, i.e., that different resolutions can be used in different frequency bands. The ideas are based on local polynomial regression and a data-driven bandwidth selector. The advantages of the proposed method are illustrated in numerical examples.