A nonparametric likelihood ratio test for the exponential series density estimator is employed as a goodness-of—fit test in the presence of nuisance parameters. These tests are designed to address the perceived weaknesses of those based on the empirical distribution function, such as the Kolmogorov-Smirnov, Cramer-von Mises and Anderson Darling tests. These tests are often criticized for not being asymptotically pivotal, having low power and offering no direction if the null hypothesis is rejected. Instead the tests of this paper are proven to be asymptotically pivotal and numerical experiments illustrate this. Further experiments suggest the tests are generally more powerful in a variety of testing problems whether bootstrap critical values are used or not. Finally, in the event of rejection, the proposed procedures involve density estimators which can be used directly and accurately to estimate quantiles.
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