Abstract
Trend estimation, i.e. estimating or smoothing a nonlinear function without any independent variables, belongs to important tasks in various applications within signal and image processing, engineering, biomedicine, analysis of economic time series, etc. We are interested in estimating trend under the presence of heteroscedastic errors in the model. So far, there seem no available studies of the performance of robust neural networks or the taut string (stretched string) algorithm under heteroscedasticity. We consider here the Aitken-type model, analogous to known models for linear regression, which take heteroscedasticity into account. Numerical studies with heteroscedastic data possibly contaminated by outliers yield improved results, if the Aitken model is used. The results of robust neural networks turn out to be especially favorable in our examples. On the other hand, the taut string (and especially its robust \(L_1\)-version) inclines to overfitting and suffers from heteroscedasticity.
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Acknowledgements
The research is supported by the projects GA19-05704S and GA18-23827S of the Czech Science Foundation. Jiří Tumpach and Patrik Janáček provided technical support.
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Kalina, J., Vidnerová, P., Tichavský, J. (2021). A Comparison of Trend Estimators Under Heteroscedasticity. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2021. Lecture Notes in Computer Science(), vol 12854. Springer, Cham. https://doi.org/10.1007/978-3-030-87986-0_8
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