Model selection procedure for high-dimensional data

For high-dimensional regression, the number of predictors may greatly exceed the sample size but only a small fraction of them are related to the response. Therefore, variable selection is inevitable, where consistent model selection is the primary concern. However, conventional consistent model selection criteria like Bayesian information criterion (BIC) may be inadequate due to their nonadaptivity to the model space and infeasibility of exhaustive search. To address these two issues, we establish a probability lower bound of selecting the smallest true model by an information criterion, based on which we propose a model selection criterion, what we call RIC_c, which adapts to the model space. Furthermore, we develop a computationally feasible method combining the computational power of least angle regression (LAR) with that of RIC_c. Both theoretical and simulation studies show that this method identifies the smallest true model with probability converging to one if the smallest true model is selected by LAR. The proposed method is applied to real data from the power market and outperforms the backward variable selection in terms of price forecasting accuracy.