PREDICTION/ESTIMATION WITH SIMPLE LINEAR MODELS: IS IT REALLY THAT SIMPLE? By

Consider the simple normal linear regression model for estimation/prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and model selection methods can be used for identifying the right model. We compare performance of such methods both theoretically and empirically from different perspectives for more insight. The testing approach, in spite of being the “standard approch”, performs poorly. We also found that the frequently told story “BIC is good when the true model is finite-dimensional and AIC is good when the true model is infinite-dimensional” is far from being accurate. In addition, despite some successes in the effort to go beyond the debate between AIC and BIC by adaptive model selection, it turns out that it is not possible to share the most essential properties of them by any model selection method. When model selection methods have difficulty in selection, model combining is seen to be a better alternative.