Fletcher-Turek Model Averaged Profile Likelihood Confidence Intervals
  We evaluate the model averaged profile likelihood confidence intervals proposed by Fletcher and Turek (2011) in a simple situation in which there are two linear regression models over which we average. We obtain exact expressions for the coverage and the scaled expected length of the intervals and use these to compute these quantities in particular situations. We show that the Fletcher-Turek confidence intervals can have coverage well below the nominal coverage and expected length greater than that of the standard confidence interval with coverage equal to the same minimum coverage. In these situations, the Fletcher-Turek confidence intervals are unfortunately not better than the standard confidence interval used after model selection but ignoring the model selection process. 
Paul Kabaila, A.H. Welsh and Waruni Abeysekera
stat.ME