Goodness of fit tests based on sup-norm statistics of empirical processes have nonstandard limiting 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 of...

In this note we consider the distributions of the Wald, likelihood ratio and Lagrange multiplier statistics in the classical linear regression model. It is shown that the finite sample distribution of each test statistic can be written as a member of the generalized beta model introduced by...

Goodness of fit tests based on empirical processes have nonstandard limiting 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 of adjusted critical...