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 (). We find a representation of the
dispersion matrix and show that the bootstrap estimator is consistent if
where
is the dimension of the parameter and
is the sample size. For fixed dimension we show that the
belongs to the
-class as defined in Liu and Singh (1992).
Key words and phrases: Bootstrap, dimension asymptotics, jackknife, many parameter regression, variance estimation.