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We discuss the main results in Estimation and Accuracy after Model Selection by
Bradley Efron. This well written article, addresses how the variability in the model
selection process can lead to unstable postselection inferences. The main result is an
easy to use, closed form formula for the standard deviation of a smoothed bootstrap
(or bagged ) estimator. A projection type argument is given in the paper to prove that
the proposed estimator is always less than or equal to the commonly used bootstrap
standard error. We investigate the validity of these results on the prostate data set, a
simulated data set where p > n, and the african data set as a representative example
for GLM. We find substantial gains in accuracy of post selection inference confidence
intervals for all subset selection, and modest gains when a regularization procedure is
used for model selection.
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