Data-driven goodness-of-fit tests

We introduce a new general class of statistical tests. The class contains Neyman's smooth tests and data-driven efficient score tests as special examples. We prove general consistency theorems for the tests from the class. The paper shows that the tests can be applied for simple and composite parametric, semi- and nonparametric hypotheses. Our tests are additionally incorporated with model selection rules. The rules allow to modify the tests by changing the penalty. Many of the optimal penalties, derived in statistical literature, can be used in our tests. This gives a hope that the proposed approach is convenient and powerful for different testing problems.