Weak Convergence of the Sample Distribution Function when Parameters are Estimated

Authors: J. Durbin - The Annals of Statistics 1973 cited by 387

The weak convergence of the sample df is studied under a given sequence of alternative hypotheses when parameters are estimated from the data. For a general class of estimators it is shown that the sample df, when normalised, converges weakly to a specified normal process. The results are specialised to the case of efficient estimation.