Testing Goodness of Fit with Multinomial Data

Several new test procedures are proposed for assessing the goodness of fit of a postulated multinomial distribution. The new tests are Neyman smooth-type tests with orders selected adaptively from the data. They are shown, through Fourier and large-sample analyses, to provide potential improvements over classical methods in terms of their ability to detect certain types of alternatives. Simulation results and a real example illustrate the finite-sample validity of the large-sample theory and the practical utility of the proposed methods.