An Exact t-Test

Multivariate linear regression and randomization-based inference are
two essential methods in statistics and econometrics. Nevertheless,
the problem of producing a randomized test for the value of a single
regression coefficient that is exactly valid when errors are exchangeable,
and which is asymptotically valid for the best linear predictor, has
remained elusive. In this paper, we produce a test that is exactly
valid with exchangeable errors and which allows for general covariate
designs; covariates may be continuous as well as discrete, and may be
correlated. The test is asymptotically valid when the errors are not
exchangeable, in particular in the presence of conditional heteroskedasticity.