A Comparison of Trend Estimators under Heteroscedasticity

Autoři: RNDr. Jan Kalina, Ph.D.
RNDr. Petra Vidnerová, Ph.D.
Jan Tichavský
Rok vydání: 2021
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Artificial Intelligence and Soft Computing. ICAISC 2021 Proceedings, Part I
Projekty: FoNeCo: Analytické základy neurovýpočtů
Schopnosti a omezení mělkých a hlubokých sítí
Bibliografická citace: KALINA, Jan, VIDNEROVÁ, Petra, TICHAVSKÝ, Jan. 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 Proceedings, Part I. Cham: Springer, 2021, S. 89-98. Lecture Notes in Artificial Intelligence, 12854. ISBN 978-3-030-87985-3. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-030-87986-0_8
DOI: 10.1007/978-3-030-87986-0_8
ID: 544026

Abstrakt

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 L1 -version) inclines to overfitting and suffers from heteroscedasticity.