On bootstrap and post-model selection inference
This paper is concerned with potential application of bootstrap methods in the context of inference after model selection. It is shown that Bootstrap methods, which are applied to solve a number of mathematically intractable problems fail within this framework. Reasons of this failure include mostly their inconsistency, asymptotic inaccuracy, correlation of estimator in each model with the indicator function, and inability for accurately estimating the model selection probabilities. Theoretical (one-way ANOVA) and practical examples (storms estimation) as well as simulations are used to illustrate the point.
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