2024/03/28 by Mayukh Choudhury, Choudhury, Mayukh, Debraj Das +1
Mathematics · Social Sciences · #FOS: Computer and information sciences #Insurance, Mortality, Demography, Risk Management #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2403.19515
openalex publication_date 2024/03/28 · openalex created_date 2024/03/30 · openalex updated_date 2026/07/28
Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate 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, the asymptotic distributional properties the Lasso estimator in GLM is still unknown. In this paper, we show that the Lasso estimator in GLM does not have a tractable form and subsequently, we develop two Bootstrap methods, namely the Perturbation Bootstrap and Pearson's Residual Bootstrap methods, for approximating the distribution of the Lasso estimator in GLM. As a result, our Bootstrap methods can be used to draw valid statistical inferences for any sub-model of GLM. We support our theoretical findings by showing good finite-sample properties of the proposed Bootstrap methods through a moderately large simulation study. We also implement one of our Bootstrap methods on a real data set.