Leverage-adjusted heteroskedastic bootstrap methods

The weighted bootstrap is a bootstrapping scheme that is valid under heteroskedasticity of unknown form. It is often used in linear regression analysis to obtain variance estimates of the ordinary least squares estimators of the linear parameters, especially when heteroskedasticity is suspected to be present in the data. Monte Carlo studies have shown, however, that its finite-sample performance can be poor when the data include points of high leverage. In this paper, we propose alternative bootstrap methods that take into the account the effect of possibly influential observations on the resulting inference via quasi-t tests. Our numerical results show that some of the proposed bootstrapping schemes generally outperform the weighted bootstrap when there are points of high leverage in the data. It is also shown that the potential gains from using the bootstrap inference we propose can be substantial. An application is presented.