Valid confidence intervals for post-model-selection predictors
By F. Bachoc, H. Leeb, B. M. Potscher. Annals of Statistics, 2014
57 citations recorded by the source corpus.
We consider inference post-model-selection in linear regression. In this setting, Berk et al.(2013) recently introduced a class of confidence sets, the so-called PoSI intervals, that cover a certain non-standard quantity of interest with a user-specified minimal coverage probability, irrespective of the model selection procedure that is being used. In this paper, we generalize the PoSI intervals to post-model-selection predictors.
Subfields: Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f794c1e6c6368e60f7fdd04439453e0575bb0484
How researchers see this paper
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In Control and Systems Engineering
- G. Alastair Young
- Daniel Garcia Rasines
- Larry A. Wasserman
- Arun K. Kuchibhotla
- Jing Lei
- Lawrence D. Brown
- M. G'Sell
- Alessandro Rinaldo
In Statistics and Probability
- Robert Tibshirani
- Larry A. Wasserman
- Jing Lei
- E.J. Candes
- M. G'Sell
- Alessandro Rinaldo
- G. Alastair Young
- Daniel Garcia Rasines
Citations in the corpus
- Uniform asymptotic inference and the bootstrap after model selection (2015, background): “Our asymptotic result holds uniformly over a wide class of nonnormal error distributions.”
- Valid post-selection inference in model-free linear regression (2020, background): “Here there exists a literature that documents the drastic effects of ignoring (P1) and (P2); see, for example, Buehler and Feddersen (1963), Olshen (1973), Rencher and Pun (1980), and Freedman (1983). We will address one particular form of problem (P1), namely, data-driven selection of regressor var”
- Splitting strategies for post-selection inference (2021, methodology): “The second group of methods includes the POSI approach of Berk et al. (2013) and extensions of it (Bachoc et al., 2017, 2020), which achieve uniformly valid inference by maximising over all possible model selection procedures, and are very conservative as a result, as well as the data splitting…”
- Bootstrapping and sample splitting for high-dimensional, assumption-lean inference (2016, methodology): “The idea is built upon by later work (Bachoc et al., 2014, 2016), which extend the ideas to other parameters of interest and which allow for heteroskedasticity, non-normality, and model misspecification.”