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 information criterion (BIC) procedure and smooth tests. The upper bound of the dimension of the exponential families in applying Schwarz's rule is allowed to grow with the number of observations to infinity. Simulation results show that the data driven version of Neyman's test performs very well for a wide range of alternatives and is competitive with other recently introduced (data driven) procedures. It is shown that the data driven smooth tests are consistent against essentially all alternatives. In proving consistency, new results on Schwarz's selection rule are derived, which may be of independent interest