Bootstrapping Lasso in Generalized Linear Models

Abstract: Generalized linear models or GLM constitute plethora of sub-models which extends the ordinary linear regression by connecting the mean of response variable with the covariates through appropriate link functions. On the other hand, Lasso is a popular and easy-to-implement penalization method in regression when not all covariates are relevant. However, Lasso does not generally have a tractable asymptotic distribution (Knight and Fu (2000)). In this paper, we develop a Bootstrap method which works as an alternative to the asymptotic distribution of Lasso for all the submodels of GLM. We support our theoretical findings by showing good finite-sample properties of the proposed Bootstrap method through a moderately large simulation study. We also implement our method on a real data set.