  Bootstrap smoothed (bagged) parameter estimators have been proposed as an
improvement on estimators found after preliminary data-based model selection.
The key result of Efron (2014) is a very convenient and widely applicable
formula for a delta method approximation to the standard deviation of the
bootstrap smoothed estimator. This approximation provides an easily computed
guide to the accuracy of this estimator. In addition, Efron (2014) proposed a
confidence interval centered on the bootstrap smoothed estimator, with width
proportional to the estimate of this approximation to the standard deviation.
We evaluate this confidence interval in the scenario of two nested linear
regression models, the full model and a simpler model, and a preliminary test
of the null hypothesis that the simpler model is correct. We derive
computationally convenient expressions for the ideal bootstrap smoothed
estimator and the coverage probability and expected length of this confidence
interval. In terms of coverage probability, this confidence interval
outperforms the post-model-selection confidence interval with the same nominal
coverage and based on the same preliminary test. We also compare the
performance of confidence interval centered on the bootstrap smoothed
estimator, in terms of expected length, to the usual confidence interval, with
the same minimum coverage probablility, based on the full model.
