Abstract
This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression. Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients. Monte Carlo simulation was conducted to verify the theoretical properties outlined in the methodology both for scenarios of presence and absence of multicollinearity and existence of outliers. The proposed procedure performed well compared to the NLS and NLTS in a viewpoint of yielding relatively lower values of MSE and Bias. Furthermore, a real data analysis demonstrated satisfactory performance of the suggested technique.
Highlights
The knowledge of nonlinear regression is one of the widely used models in analyzing the effect of explanatory variables on a response variable
Zucker et al [19] developed an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation and Hang et al [6] proposed a graph regularized nonlinear ridge regression (RR) model for remote sensing data analysis, including hyper-spectral image classification and atmospheric aerosol retrieval
Monte Carlo study is conducted to investigate the behaviour of the proposed Nonlinear Least Trimmed Squares estimator (NLTS)-Elnet estimator on simulated and real data with a comparison of its performance to Nonlinear Least Squares criterion (NLS) and NLTS
Summary
The knowledge of nonlinear regression is one of the widely used models in analyzing the effect of explanatory variables on a response variable. Zucker et al [19] developed an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation and Hang et al [6] proposed a graph regularized nonlinear ridge regression (RR) model for remote sensing data analysis, including hyper-spectral image classification and atmospheric aerosol retrieval. These regularization methods have shown exceptional performance in various fields, it uses the least squares loss function which is influenced by outliers [12].
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