On various confidence intervals post-model-selection
By H. Leeb, B. M. Potscher, K. Ewald. 2014
60 citations recorded by the source corpus.
We compare several confidence intervals after model selection in the setting recently studied by Berk et al. (2013), where the goal is to cover not the true parameter but a certain non-standard 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.
Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ff3946e9298d342f9fa54e55e5dfa7ea71f18372
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In Artificial Intelligence
In Control and Systems Engineering
- F. Bachoc
- H. Leeb
- B. M. Potscher
- Tae-Hwy Lee
- Richard A. Berk
- Patrik Guggenberger
- Serena Ng
- Donald W. K. Andrews
In Statistics and Probability
Citations in the corpus
- Predicting the long-term stock market volatility: A GARCH-MIDAS model with variable selection (2020, background): “The variable selection can have a detrimental impact on the subsequently constructed inference procedures, such as confidence intervals, if these are constructed in a “naïve” way where the model selection is ignored (Berk et al., 2013; Leeb et al., 2015).”
- Valid confidence intervals for post-model-selection predictors (2014, methodology): “Similar as in Berk et al. (2013a) and Leeb et al. (2013), we refer to the data set obtained in the second case as the exchangeable data set, and to the one obtained in the third case as the equicorrelated data set.”