A0422
Title: Bootstrapping Lasso in generalized linear models for large dimension under variable selection consistency
Authors: Mayukh Choudhury - Indian Institute of Technology Bombay (India) [presenting]
Debraj Das - Indian Institute of Technology Bombay (India)
Abstract: GLM constitutes a plethora of sub-models that extend the ordinary linear regression by connecting the mean of the response variable with the covariates through link functions. On the other hand, Lasso is a popular and easy-to-implement penalization method for selecting important covariates in regression when not all of them are relevant. However, Lasso generally has a complicated asymptotic distribution even when $p$ is fixed. Hence, a perturbation bootstrap (PB) method is developed, which approximates the asymptotic distribution of Lasso in GLM. We will first discuss the asymptotic distribution of properly centered and scaled GLM estimator when parameter dimension $d$ increases at slower rate than $n$. In a later regime, when $d>>n$, we employ sparsity in the model, typically Lasso in GLM. when the penalty sequence $n^{-1/2}\lambda_n\to\infty$, considering Lasso to be VSC, it is proven that Gaussian approximation fails to this end for properly centered and scaled Lasso estimator. As an alternative, a PB-Lasso estimator is established to mimic the distribution through a Berry-Eseen type bound uniformly over the class of measurable convex sets. The theoretical findings are supported by showing good finite-sample properties of the proposed bootstrap method through a large simulation study.
