Uniformly valid confidence intervals post-model-selection

By F. Bachoc, David Preinerstorfer, Lukas Steinberger. Annals of Statistics, 2016

53 citations recorded by the source corpus.

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory we apply our methods to practically important situations where the candidate set of models, from which a working model is selected, consists of fixed design homoskedastic or heteroskedastic linear models, or of binary regression models with general link functions. In an extensive simulation study, we find that the proposed confidence intervals perform remarkably well, even when compared to existing methods that are tailored only for specific model selection procedures.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8717b39679c51c24f7f6cdea526f8c3a806ffb85

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Citations in the corpus

Valid confidence intervals for post-model-selection predictors (2014, background): “] For ways to work around this assumption on ̂(2) by using conservative estimators for the variance see Bachoc et al. (2016).”
Bootstrapping and sample splitting for high-dimensional, assumption-lean inference (2016, methodology): “[6] François Bachoc, David Preinerstorfer, and Lukas Steinberger.”
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…”