Bootstrapping and sample splitting for high-dimensional, assumption-lean inference

By Alessandro Rinaldo, Larry A. Wasserman, M. G'Sell, Jing Lei. Annals of Statistics, 2016

111 citations recorded by the source corpus.

Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting combined with the bootstrap (or the Normal approximation). We show that this leads to a simple, assumption-free approach to inference and we establish results on the accuracy of the method. In fact, we find new bounds on the accuracy of the bootstrap and the Normal approximation for general nonlinear parameters with increasing dimension which we then use to assess the accuracy of regression inference. We show that an alternative, called the image bootstrap, has higher coverage accuracy at the cost of more computation. We define new parameters that measure variable importance and that can be inferred with greater accuracy than the usual regression coefficients. There is a inference-prediction tradeoff: splitting increases the accuracy and robustness of inference but can decrease the accuracy of the predictions.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7bfe4f9c87da684da2ffe3cfd48f3c24dc75b8dd

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Citations in the corpus

Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices (2019, background): “In addition, while we focus on mean-squared prediction error, diﬀerent criteria can be considered, as in the predictive inference literature [RWG19].”
Generic Machine Learning Inference on Heterogenous Treatment Effects in Randomized Experiments (2017, unknown): “The premise is the same, however, as in [42, 45] – we should not rely on a single random split of the data and should adjust inference in some way.”
Uniformly valid confidence intervals post-model-selection (2016, methodology): “This confidence interval is developed for the lasso model selector and has some asymptotic guarantees which are discussed in Taylor and Tibshirani (2017).”
Splitting strategies for post-selection inference (2021, methodology): “In the randomdesign case, Rinaldo et al. (2019) develop inferential methods for other choices of the selected parameter which depend on the distribution of the covariates.”