DATA-DRIVEN SMOOTH TESTS WHEN THE HYPOTHESIS IS COMPOSITE

In recent years several authors have recommended smooth tests for rest ing goodness of fit. However, the number of components in the smooth t est statistic should be chosen well; otherwise, considerable loss of p ower may occur. Schwarz's selection rule provides one such good choice . Earlier results on simple null hypotheses are extended here to compo site hypotheses, which tend to be of mure practical interest. For gene ral composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testi ng exponentiality and normality show-that the data-driven version of N eyman's test compares well to other, even specialized, tests over a wi de range of alternatives.