BOOTSTRAPPING AND EMPIRICAL EDGEWORTH EXPANSIONS IN MULTIPLE LINEAR-REGRESSION MODELS

A general asymptotic expansion for the distribution of the studentized least squares estimate in multiple linear regression models is obtained without assuming normal errors and under simple easily verifiable conditions. This expansion provides a better than the normal approximation for estimation and testing. It is also shown that the bootstrap approximation for the distribution of the studentized least squares estimate has a valid asymptotic expansion and this shows that the bootstrap is better than the normal for approximating the distribution of the studentized least squares estimate. A comparison between the bootstrap approximation and the empirical Edgeworth expansion is also provided showing that the bootstrap approximation for the distribution of the studentized least squares estimate is better than the two-term Edgeworth expansion.