A Simple Method for Testing Goodness of Fit in the Presence of Nuisance Parameters

Summary This paper presents a method, based on the empirical distribution function, for testing goodness of fit (gf) under composite null hypotheses. After the unknown parameters are estimated from the entire data set, the procedure calls for the transformed sample to be randomly partitioned into a large number of groups, and a gf statistic calculated for each group. These statistics are used to construct a test which can attain, asymptotically, any desired level α, and which requires for its implementation only standard tables of critical values. The procedure is particularly recommended when an a priori grouping of the sample can be employed and, hence, heterogeneous alternatives are quite plausible. It is shown that, under these alternatives, the power of the procedure compares favourably with that of other methods.