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B1665
Title: Inference in high-dimensional linear models with the bootstrap Authors:  Karl Gregory - University of South Carolina (United States) [presenting]
Soumendra Lahiri - North Carolina State University (United States)
Abstract: Bootstrap is studied in the context of the high-dimensional linear regression model, in which the number of predictors is very large compared to the sample size. We concern ourselves with the sparse setting, in which many predictors do not influence the response, but the number of predictors which do influence the response is regarded as growing with the sample size. In this setting we consider applying the bootstrap to variants of Lasso-type estimators. We consider the de-sparsified Lasso estimator, which is asymptotically Normal under mild conditions and allows for the construction of confidence intervals for individual regression coefficients in the high-dimensional linear regression model. This estimator is ground-breaking in that it allows one to make inference on the regression coefficients of the active as well as of the inactive predictors without necessitating strong conditions. We explore ways to improve the finite-sample coverage accuracy of confidence intervals in the high-dimensional linear model setting via application of the bootstrap.