Model selection in linear regression using paired bootstrap

Model selection is an important and challenging problem in statistics. The model selection is inevitable in a large number of applications including life sciences, social sciences, business, or economics. In this article, we propose a resampling-based information criterion called paired bootstrap criterion (PBC) for model selection. The proposed criterion is based on minimizing the conditional expected prediction loss for selecting the best subset of variables. We estimate the conditional expected prediction loss by using the out-of-bag (OOB) bootstrap approach. Other classical criteria for model selection such as AIC, BIC are also presented for comparison purpose. We demonstrate that the proposed paired bootstrap model selection criterion is effective in selecting accurate models via real and simulated data examples. The results confirm the satisfactory behavior of the proposed model selection criterion to select parsimonious models that fit the data well. We apply the proposed methodology to a real data example.