Heteroskedasticity–robust tests with minimum size distortion

Asymptotically valid inference in linear regression models is easily achieved under mild conditions using the well-known Eicker–White heteroskedasticity–robust covariance matrix estimator or one of its variant. In finite sample however, such inferences can suffer from substantial size distortion. Indeed, it is well established in the literature that the finite sample accuracy of a test may depend on which variant of the Eicker–White estimator is used, on the underlying data generating process (DGP) and on the desired level of the test.This paper develops a new variant of the Eicker–White estimator which explicitly aims to minimize the finite sample null error in rejection probability (ERP) of the test. This is made possible by selecting the transformation of the squared residuals which results in the smallest possible ERP through a numerical algorithm based on the wild bootstrap. Monte Carlo evidence indicates that this new procedure achieves a level of robustness to the DGP, sample size and nominal testing level unequaled by any other Eicker–White estimator based asymptotic test.