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高维惩罚回归中具有高阶精度的对称 Bootstrap 置信区间AI 解读

This article develops methodology for higher order accurate two-sided Bootstrap confidence intervals (CIs) in high dimensional penalized regression models using the Bootstrap. We consider a large class of penalized regression methods that satisfy the Oracle property of Fan and Li and a stronger variant of it, called the Strong Oracle property. While second order accuracy of the Bootstrap is known for both classes, it is typically not sufficient to guarantee better accuracy…

通过扰动自助法实现 lasso 的分布一致性AI 解读

Summary The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the…

自适应 Lasso 的扰动自助法AI 解读

The Adaptive Lasso (Alasso) was proposed by Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] as a modification of the Lasso for the purpose of simultaneous variable selection and estimation of the parameters in a linear regression model. Zou [J. Amer. Statist. Assoc. 101 (2006) 1418–1429] established that the Alasso estimator is variable-selection consistent as well as asymptotically Normal in the indices corresponding to the nonzero regression coefficients in certain…