Iterative Adaptive Robust Variable Selection in Nomparametric Additive Models

By utilizing the robust loss function, B-spline approximation and adaptive group Lasso, a nonparametric additive model is investigated to identify insignificant covariates for the ``large p small n'' setting. Compared with the ordinary least-square adaptive group Lasso, the proposed method is resistant to heavy-tailed errors or outlines in the responses. To prove facilitate presentation, a more general weighted robust group Lasso estimator is considered. Moreover, the weight vectors play a pivotal role for the suggested estimators to enjoy the model selection oracle property and asymptotic normality. The robust group Lasso and adaptive robust group Lasso can be seen as special circumstances of different weight vectors. In practice, we use the robust group Lasso to obtain an initial estimator to reduce the dimension of the problem, and then apply the iterative adaptive robust group Lasso to select nonzero components. The results of simulation studies show that the proposed methods work well with samples of moderate size.\! A high-dimensional gene TRIM32 data is used to illustrate the application of the proposed method.