Variable selection for additive model via cumulative ratios of empirical strengths total

We propose a data-driven method to select significant variables in additive model via spline estimation. The additive structure of the regression model is imposed to overcome the ‘curse of dimensionality’, while the spline estimators provide a good approximation to the additive components of the model. The additive components are ordered according to their empirical strengths, and the significant variables are chosen at the first crossing of a predetermined threshold by the CUmulative Ratios of Empirical Strengths Total of the components. Consistency of the proposed method is established when the number of variables are allowed to diverge with sample size, while extensive Monte-Carlo study demonstrates superior performance of the proposed method and its advantages over the BIC method of Huang and Yang [(2004), ‘Identification of Nonlinear: Additive Autoregressive Models’, Journal of the Royal Statistical Society Series B, 66, 463–477] in terms of speed and accuracy.