Variance estimation in high dimensional regression models

Abstract

We treat the problem of variance estimation of the least squares estimate of the parameter in high dimensional linear regression models by using the Uncorrelated Weights Bootstrap (UBS). We find a representation of the UBS dispersion matrix and show that the bootstrap estimator is consistent if p²/n→ 0 where p is the dimension of the parameter and n is the sample size. For fixed dimension we show that the UBS belongs to the R-class as defined in Liu and Singh (1992).