Statistical learning for recommending (robust) nonlinear regression methods

0511819 - ÚI 2020 RIV SK eng J - Článek v odborném periodiku
Kalina, Jan - Tichavský, Jan
Statistical learning for recommending (robust) nonlinear regression methods.
Journal of applied mathematics, statistics and informatics. Roč. 15, č. 2 (2019), s. 47-59. ISSN 1336-9180
Grant CEP: GA ČR(CZ) GA19-05704S
Grant ostatní: GA ČR(CZ) GA17-07384S
Institucionální podpora: RVO:67985807
Klíčová slova: Statistical learning * Nonlinear regression * Robustness * Heteroscedasticity * nonlinear least weighted squares * optimal method selection * optimization * computations
Obor OECD: Statistics and probability
Způsob publikování: Open access

We are interested in comparing the performance of various nonlinear estimators of parameters of the standard nonlinear regression model. While the standard nonlinear least squares estimator is vulnerable to the presence of outlying measurements in the data, there exist several robust alternatives. However, it is not clear which estimator should be used for a given dataset and this question remains extremely di cult (or perhaps infeasible) to be answered theoretically. Metalearning represents a computationally intensive methodology for optimal selection of algorithms (or methods) and is used here to predict the most suitable nonlinear estimator for a particular dataset. The classi cation rule is learned over a training database of 24 publicly available datasets. The re- sults of the primary learning give an interesting argument in favor of the nonlinear least weighted squares estimator, which turns out to be the most suitable one for the majority of datasets. The subsequent metalearning reveals that tests of normality and heteroscedasticity play a crucial role in nding the most suitable nonlinear estimator.
Trvalý link: http://hdl.handle.net/11104/0302064