Selective inference in regression models with groups of variables
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Abstract (arXiv)
We provide a general mathematical framework for selective inference with supervised model selection procedures characterized by quadratic forms in the outcome variable. Forward stepwise with groups of variables is an important special case as it allows models with categorical variables or factors. Models can be chosen by AIC, BIC, or a fixed number of steps. We provide an exact significance test for each group of variables in the selected model based on an appropriately truncated chi or F distribution for the cases of known and unknown σ2 respectively. An efficient software implementation is available as a package in the R statistical programming language.
Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Nov 2015.
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Citing papers per year: 2021: 4; 2022: 4; 2023: 0; 2024: 0; 2025: 1.
9 papers.
- 2022Selective inference for k-means clusteringcited by 22
- 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuationcited by 16
- 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Modelcited by 15
- 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inferencecited by 10
- 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inferencecited by 7
- 2025Change Point Detection in the Frequency Domain with Statistical Reliabilitycited by 2
- 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detectioncited by 0
- 2022Inferring independent sets of Gaussian variables after thresholding correlationscited by 0
- 2022Neural Networks beyond explainability: Selective inference for sequence motifscited by 0
- 2025Change Point Detection in the Frequency Domain with Statistical Reliability5 Feb 2025
- 2022Neural Networks beyond explainability: Selective inference for sequence motifs23 Dec 2022
- 2022Inferring independent sets of Gaussian variables after thresholding correlations2 Nov 2022
- 2022Selective inference for k-means clustering29 Mar 2022
- 2022Statistical Inference for the Dynamic Time Warping Distance, with Application to Abnormal Time-Series Detection14 Feb 2022
- 2021Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference18 Oct 2021
- 2021Exact Statistical Inference for the Wasserstein Distance by Selective Inference29 Sep 2021
- 2021Fast and More Powerful Selective Inference for Sparse High-order Interaction Model9 Jun 2021
- 2021Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation22 Apr 2021