CONSISTENCY AND MONTE-CARLO SIMULATION OF A DATA-DRIVEN VERSION OF SMOOTH GOODNESS-OF-FIT TESTS

The data driven method of selecting the number of components in Neyman 's smooth test for uniformity, introduced by Ledwina, is extended. The resulting tests consist of a combination of Schwarz's Bayesian inform ation criterion (BIG) procedure and smooth tests. The upper bound of t he dimension of the exponential families in applying Schwarz's rule is allowed to grow with the number of observations to infinity. Simulati on results show that the data driven version of Neyman's test performs very well for a wide range of alternatives and is competitive with ot her recently introduced (data driven) procedures. It is shown that the data driven smooth tests are consistent against essentially all alter natives. In proving consistency, new results on Schwarz's selection ru le are derived, which may be of independent interest.