Robust estimation based on B-splines with simultaneous variable selection for partially linear additive models

MARTINEZ, ALEJANDRA MERCEDES; MURRONE, NICOLÁS

Londres

Congreso; 15th International Conference of the ERCIM WG on Computational and Methodological Statistics and 16th International Conference on Computational and Financial Econometrics; 2022

To deal with the curse of dimensionality, partially linear additive models provide a flexible and interpretable approach to building predictive models. Under these models, the response variable depends linearly on some covariates, while the others enter the model in a fully nonparametric way, as a sum of univariate functions of each variable, that is, as an additive model. In practice, a large number of covariates may be collected, and the non-significative ones should be excluded from the model. For that reason, it is important to automatically select variables either in the parametric or in the nonparametric components. In order to obtain simultaneously robust estimators and select the active covariates, we introduce a family of robust estimators that combines B-splines and robust regression estimators with a regularization procedure based on a SCAD penalty which penalizes both the coefficients of the linear and additive components. Through a Monte Carlo study, we will show the advantage of the proposed methodology with respect to that based on least squares.