Goodness of fit tests based on sup-norm statistics of empirical processes have nonstandard limit- ing distributions when the null hypothesis is composite — that is, when parameters of the null model are estimated. Several solutions to this problem have been suggested, including the calculation...

The Wald, likelihood ratio and Lagrange multiplier test statistics are commonly used to test linear restrictions in regression models. It is shown that for testing these restrictions in the classical regression model, the exact densities of these test statistics are special cases of the...