Identification for partially linear regression model with autoregressive errors

Kazemi, Mohammad; Shahsvani, D.; Arashi, Mohammad; Rodrigues, Paulo Canas

doi:10.1080/00949655.2020.1857763

Cited by 1 publication

(1 citation statement)

References 27 publications

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“…[26] introduced a similar additive model and they enforced linearity to the spline approximation of the functions using the group penalty function of the second derivative of the B-splines. There are also more contributions on the problem of structure recognition and separation of nonlinear and linear parts of the SLA model [27,28]. Some details of the literature review for the proposed separation approaches are considered in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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

Amini,

Roozbeh,

Mohamed

2024

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%