Separation of the Linear and Nonlinear Covariates in the Sparse Semi-Parametric Regression Model in the Presence of Outliers

Morteza Amini, Mahdi Roozbeh () and Nur Anisah Mohamed ()
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Morteza Amini: Department of Statistics, School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran P.O. Box 14155-6455, Iran
Mahdi Roozbeh: Department of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan P.O. Box 35195-363, Iran
Nur Anisah Mohamed: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2024, vol. 12, issue 2, 1-17

Abstract: Determining the predictor variables that have a non-linear effect as well as those that have a linear effect on the response variable is crucial in additive semi-parametric models. This issue has been extensively investigated by many researchers in the area of semi-parametric linear additive models, and various separation methods are proposed by the authors. A popular issue that might affect both estimation and separation results is the existence of outliers among the observations. In order to address this lack of sensitivity towards extreme observations, robust estimating approaches are frequently applied. We propose a robust method for simultaneously identifying the linear and nonlinear components of a semi-parametric linear additive model, even in the presence of outliers in the observations. Additionally, this model is sparse in that it may be used to determine which explanatory variables are ineffective by giving accurate zero estimates for their coefficients. To assess the effectiveness of the proposed method, a comprehensive Monte Carlo simulation study is conducted along with an application to investigate the dataset, which includes Boston property prices dataset.

Keywords: adaptive LASSO; group LASSO; outlier; penalized approaches; robust methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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