Additive models are flexible nonparametric models. Finding the nonzero additive components when the true model is assumed to be sparse is an important problem and is well studied. The existing research focused on using the \(L_2\) loss function, which is sensitive to outliers in the data. We propose a new variable selection method for additive models that is robust to outliers in the data. It considers the framework of B-splines and density power divergence loss function for estimation, and employs a nonconcave penalty for variable selection. Our asymptotic results are derived under the sub-Weibull assumption, which allows the error distribution to have an exponentially heavy tail. Under regularity conditions, we show that the proposed method achieves the optimal convergence rate. Our results include the convergence rates for sub-Gaussian and sub-Exponential distributions as special cases. We numerically validate the theoretical findings using simulations and real data analysis.
