DATA-DRIVEN VERSION OF NEYMANS SMOOTH TEST OF FIT

Neyman's smooth test for testing uniformity is a recognized goodness-o f-fit procedure. As stated by LaRiccia, the test can be viewed as a co mpromise between omnibus test procedures, with generally low power in all directions, and procedures whose power is focused in the direction of a specific alternative. The basic idea behind this test is to embe d the null density into, say, a k-dimensional exponential family and t hen to construct an asymptotically optimal test for the parametric tes ting problem. The resulting procedure is Neyman's test with k componen ts. The most difficult problem related with using this test is the cho ice of k. Recommendations in statistical literature are sometimes conf using. Some authors advocate a small number of components, whereas oth ers show that in some situations a larger number of components is prof itable. All existing suggestions concerning how to select k exploit in fact some preliminary knowledge about a possible alternative. In this article, a new data-driven method for selecting the number of compone nts in Neyman's test is proposed. The method consists of using Schwarz 's BIC procedure to choose the dimension of the exponential model for the data and then using the chosen dimension as the number of componen ts. So this novel procedure relies on fitting the model to the data an d verifying whether the difference between the model and the uniform d istribution is significant. Consistency of the method is proved. Prese nted simulations show that the test adapts well to the alternative at hand. Simulated power of the data-driven version of Neyman's test also performs well in comparison with that of other tests.