Abstract
Typical modeling strategies involve model selection, which has a significant effect on inference of estimated parameters. Common practice is to use a selected model ignoring uncertainty introduced by the process of model selection. This could yield overoptimistic inferences, resulting in false discovery. In this article we develop a general methodology via optimal approximation for estimating the mean and variance of complex statistics that involve the process of model selection. This allows us to make approximately unbiased inferences, taking into account the selection process. We examine the operating characteristics of the proposed methodology via asymptotic analyses and simulations. These results show that the proposed methodology yields correct inferences and outperforms common alternatives.