A class of pseudo distances is used to derive test statistics using transformed\ndata or spacings for testing goodness-of-fit for parametric models. These statistics\ncan be considered as density based statistics and expressible as simple\nfunctions of spacings. It is known that when the null hypothesis is simple, the\nstatistics follow asymptotic normal distributions without unknown parameters.\nIn this paper we emphasize results for the null composite hypothesis: the\nparameters can be estimated by a generalized spacing method (GSP) first\nwhich is equivalent to minimize a pseudo distance from the class which is\nconsidered; subsequently the estimated parameters are used to replace the\nparameters in the pseudo distance used for estimation; goodness-of-fit statistics\nfor the composite hypothesis can be constructed and shown to have again\nan asymptotic normal distribution without unknown parameters. Since these\nstatistics are related to a discrepancy measure, these tests can be shown to be\nconsistent in general. Furthermore, due to the simplicity of these statistics\nand they come a no extra cost after fitting the model, they can be considered\nas alternative statistics to chi-square statistics which require a choice of intervals\nand statistics based on empirical distribution (EDF) using the original\ndata with a complicated null distribution which might depend on the parametric\nfamily being considered and also might depend on the vector of true\nparameters but EDF tests might be more powerful against some specific\nmodels which are specified by the alternative hypothesis.
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