Heteroskedasticity-Robust Tests in Regression Directions

We develop simple procedures to test for omitted variables and perform other tests in regression directions, which are asymptotically valid in the presence of heteroskedasticity of unknown form. We examine the asymptotic behaviour of these tests, and use Edgeworth approximations to study their approximate finite-sample performance. We also present results from several Monte Carlo experiments, which suggest that one family of these tests should always be used in preference to the other.