# Distributional Consistency of Lasso by Perturbation Bootstrap

arXiv: https://arxiv.org/abs/1710.10709 · HTML: https://mlsanity.com/paper/1710.10709/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [Error Controlled Feature Selection for Ultrahigh Dimensional and Highly Correlated Feature Space Using Deep Learning](https://mlsanity.com/paper/2209.07011/) (2022)

## Abstract (arXiv)

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.