Univariate measurement error selection likelihood for variable selection of additive model

In this paper, we introduce a measurement error selection likelihood to select important variables and estimate additive components simultaneously in a high-dimensional additive model. Although the model contains multi-variates, the proposed estimation is a type of univariate nonparametric form. This format matches the feature of the additive structure in the sense that both the model and the nonparametric estimation are of univariate nonparametric feature, essentially. Consequently, the variable selection is valid even if the number of variables is large. The selection consistency is obtained and finite performances are illustrated via Monte Carlo experiments.