Distributional Consistency of Lasso by Perturbation Bootstrap

29 Oct 2017  ·  Das Debraj, Lahiri S. N. ·

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. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Methodology Statistics Theory Statistics Theory

Datasets


  Add Datasets introduced or used in this paper