Comparison of bootstrap and jackknife variance estimators in linear regression: Second order results

In an extension of the work of Liu and Singh (1992), we consider resampling estimates for the variance of the least squares estimator in linear regression models. Second order terms in asymptotic expansions of these estimates are derived. By comparing the second order terms, certain generalised bootstrap schemes are seen to be theoretically better than other resampling techniques under very general conditions. The performance of the different resampling schemes are studied through a few simulations.