Mayukh Choudhury, IIT Bombay

Annual Progress Seminar
Wednesday, 27th September 2023, 3.00 pm
Venue: Ramanujan Hall

Host: Debraj Das

Speaker: Mr. Mayukh Choudhury
Affiliation: IIT Bombay

Title: Bootstrapping LASSO in Generalized Linear Models
Abstract: Generalized linear models or GLM is an important set of models 
that generalizes the ordinary linear regression by connecting the 
response variable with the covariates through arbitrary link functions 
and thus allowing the responses to have arbitrary distributions. On the 
other hand, the Least Absolute Shrinkage and Selection Operator or the 
Lasso is a popular and easy-to-implement penalization method in 
regression especially when all the covariates are not relevant. However, 
Lasso has complicated asymptotic distribution which is not useful in 
practice and hence development of an alternative method of 
distributional approximation is required for the purpose of statistical 
inference. Bootstrap generally works as an alternative in most of the 
inference problems. In that spirit, here we develop a Bootstrap method 
that works as an approximation of the distribution of the Lasso 
estimator for all the sub-models of GLM. However, it is the usual 
practice that cross-validation is used to choose a data-dependent choice 
of the penalty parameter in Lasso. To bridge the gap between the 
developed Bootstrap theory and the use of cross-validation, we also 
establish the asymptotic property of the K-fold cross-validated choice 
of the penalty parameter.
Ramanujan Hall, Department of Mathematics
Wed, September 27, 2023
Start Time
3:00pm IST
Created by
Mon, September 25, 2023 10:28am IST