Expected length of post-model-selection confidence intervals conditional on polyhedral constraints
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Valid inference after model selection is currently a very active area of research. The polyhedral method, pioneered by Lee et al. (2016), allows for valid inference after model selection if the model selection event can be described by polyhedral constraints. In that reference, the method is exemplified by constructing two valid confidence intervals when the Lasso estimator is used to select a model. We here study the expected length of these intervals. For one of these confidence intervals, that is easier to compute, we find that its expected length is always infinite. For the other of these confidence intervals, whose computation is more demanding, we give a necessary and sufficient condition for its expected length to be infinite. In simulations, we find that this condition is typically satisfied.
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