Lectures 2 and 3 - Goodness - of - Fit ( GoF ) Tests

Often times we have some data and want to test if a particular statistical model (or model class) is a good fit. For instance, it is common to make normality assumptions about certain kinds of data for simplicity. Nevertheless one must check if these assumptions are reasonable. In Goodness-of-Fit (GoF) testing we strive to check the compatibility of the data with a fixed single model (simple GoF) or with a model in a given class (composite GoF). Let X1, . . . , Xn be i.i.d. samples from an unknown distribution F . If we wish to infer whether this sample comes from a certain hypothesized distribution F0 the problem can be cast as the following hypothesis test: H0 : F = F0 vs. H1 : F 6= F0 .