  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.
