Distributional Consistency of Lasso by Perturbation Bootstrap

Debraj Das; S. N. Lahiri

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arXiv · 1710.10709

Distributional Consistency of Lasso by Perturbation Bootstrap

Debraj Das·S. N. Lahiri

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Abstract

Least Absolute Shrinkage and Selection Operator or the Lasso, introduced by Tibshirani (1996), is a popular estimation procedure in multiple linear regression when underlying design has a sparse structure, because of its property that it sets some regression coefficients exactly equal to 0. In this article, we develop a perturbation bootstrap method and establish its validity in approximating the distribution of the Lasso in heteroscedastic linear regression. We allow the underlying covariates to be either random or non-random. We show that the proposed bootstrap method works irrespective of the nature of the covariates, unlike the resample-based bootstrap of Freedman (1981) which must be tailored based on the nature (random vs non-random) of the covariates. Simulation study also justifies our method in finite samples.

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Debraj Das, S. N. Lahiri. 2017-10-29. Distributional Consistency of Lasso by Perturbation Bootstrap. https://arxiv.org/abs/1710.10709

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