Detail
On Various Confidence Intervals Post-Model-Selection
- Author(s)
- Hannes Leeb, Benedikt Pötscher, Karl Ewald
- Abstract
We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [Ann. Statist. 41 (2013) 802-837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the "naive" confidence interval, which is constructed as if the selected model were correct and fixed a priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.
- Organisation(s)
- Department of Statistics and Operations Research
- External organisation(s)
- Technische Universität Wien
- Journal
- Statistical Science
- Volume
- 30
- Pages
- 216-227
- No. of pages
- 12
- ISSN
- 0883-4237
- Publication date
- 2015
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101018 Statistics
- Keywords
- ASJC Scopus subject areas
- Mathematics(all), Statistics and Probability, Statistics, Probability and Uncertainty
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/on-various-confidence-intervals-postmodelselection(cb0ad11a-8441-403b-8bb7-83d01ca0e247).html