Distribution free bootstrap prediction intervals after variable selection

Abstract

In this paper, we propose two new prediction intervals for linear regression models after variable selection. One of the benefits of the proposed prediction intervals compared to most existing ones is that the distribution of the errors does not need to be known. The asymptotic constancy of the proposed prediction intervals was also examined and showed that the predictions are asymptotically optimal. Simulations were used to illustrate that the new intervals are able to produce better predictions even for sparse models. We compare the new prediction intervals with a few widely used prediction intervals in terms of their achieved coverage and length.