A Randomized Bootstrap Approach to Overcoming Model Selection Uncertainty

Abstract: Statistical inference is traditionally based on the assumption that one single model is the true model, whereas in fact several models could fit the data equally well. Following this common practice means that model selection uncertainty is ignored, with the result of biased estimates and too narrow intervals. In this thesis we study criteria for model selection and introduce a bootstrap approach where a model is selected at random, based on measures of fit of the contending models. This method is tested in a simulation study, where we estimate the 10th percentile, and is compared with an available method developed by Buckland et al. (1997). We also consider the situation where the true model is known and no model selection procedure is applied, with the purpose of evaluating the effect of model selection. We find that model selection yields broader intervals with good coverage and that the parametric two-step variant of the proposed randomized bootstrap approach is an applicable method for overcoming model selection uncertainty.