2018/03/05 by Danijel Kivaranovic, Kivaranovic, Danijel, Hannes Leeb +1
Mathematics · #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1803.01665
openalex publication_date 2018/03/05 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
Valid inference after model selection is currently a very active area of\nresearch. The polyhedral method, pioneered by Lee, et al. (2016), allows for\nvalid inference after model selection if the model selection event can be\ndescribed by polyhedral constraints. In that reference, the method is\nexemplified by constructing two valid confidence intervals when the Lasso\nestimator is used to select a model. We here study the length of these\nintervals. For one of these confidence intervals, which is easier to compute,\nwe find that its expected length is always infinite. For the other of these\nconfidence intervals, whose computation is more demanding, we give a necessary\nand sufficient condition for its expected length to be infinite. In\nsimulations, we find that this sufficient condition is typically satisfied,\nunless the selected model includes almost all or almost none of the available\nregressors. For the distribution of confidence interval length, we find that\nthe \κ-quantiles behave like 1/(1-\κ) for \κ close to 1.\nOur results can also be used to analyze other confidence intervals that are\nbased on the polyhedral method.\n