ABSTRACT
Many different methods for testing exist in the literature. The common feature of most of these methods is that the observations are assumed to be independent. Critical values for test statistics are derived under this assumption. Simulated rejection probabilities for the Kolmogorov-Smirnov test statistic in the simple hypothesis case, with critical values derived under independence for the level of significance 0.05. The first remark yields an additional explanation to the well-known phenomenon that for large samples, goodness of fit tests always tend to reject the null hypothesis. Analogous limit theorems can be derived for the case of composite hypothesis. An analogous limit theorem can be obtained under certain types of alternatives.
