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The L1-type regularization methods have drawn a large amount of attention for not only linear but also nonlinear regression modeling. By imposing lasso type penalties, the L1-type regularization metho...ds effectively select the number of basis functions, and thus we can perform well capturing the complex structure of data in nonlinear regression modeling. Although the L1-type regularization approaches have been successfully used in various fields of research, their performances take a sudden turn for the worst in the presence of outliers, since the lasso type approaches are based on least squares or maximum likelihood estimator. To settle on the issue, we propose robust regularization methods for nonlinear regression modeling based on a novel least trimmed squares estimation. The proposed least trimmed squares regularization methods perform regression modeling based on s observations identified as non-outliers by outlier detection measures, and thus we can effectively perform robust nonlinear regression modeling without masking and swamping effects of outliers. We illustrate through Monte Carlo simulations and real world example that the proposed robust strategy effectively performs nonlinear regression modeling, even in the presence of outlier.show more
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