Inference for sparse linear regression based on the leave-one-covariate-out solution path

Xiangyang Cao, Karl Gregory and Dewei Wang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 18, 6640-6657

Abstract: We propose a new measure of variable importance in high-dimensional regression based on the change in the LASSO solution path when one covariate is left out. The proposed procedure provides a novel way to calculate variable importance and conduct variable screening. In addition, our procedure allows for the construction of p-values for testing whether each coefficient is equal to zero as well as for testing hypotheses involving multiple regression coefficients simultaneously; bootstrap techniques are used to construct the null distribution. For low-dimensional linear models, our method can achieve higher power than the t-test. Extensive simulations are provided to show the effectiveness of our method. In the high-dimensional setting, our proposed solution path based test achieves greater power than some other recently developed high-dimensional inference methods. We extend our method to logistic regression and demonstrate in simulation that our leave-one-covariate-out solution path tests can provide accurate p-values.

Date: 2023
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DOI: 10.1080/03610926.2022.2032171

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