A0554
Title: HC3 standard errors for the debiased lasso
Authors: Akira Shinkyu - Shiga University (Japan) [presenting]
Abstract: The debiased Lasso is investigated in high-dimensional linear regression, where conditional error variances can be heteroskedastic. Numerical experiments indicate that existing heteroskedasticity-consistent variance estimators and standard errors for the debiased Lasso tend to become underestimates, and thus, confidence intervals tend to yield small coverages. To address this problem, an HC3-type variance estimator and standard error are proposed for the debiased Lasso. Theoretical analysis shows that the proposed variance estimator is never downward biased for the variance of normally random part in the debiased Lasso and consistent for the asymptotic variance of the debiased Lasso under some conditions. Simulation studies show that the proposed standard error significantly improves coverages of confidence intervals by the debiased Lasso, and these confidence intervals have more accurate coverages than those obtained by existing methods, particularly when conditional error variances are heteroskedastic.
