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.