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Model selection, large deviations and consistency of data-driven tests

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84039

Langovoy,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Langovoy, M.(2009). Model selection, large deviations and consistency of data-driven tests (2009-007).


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-C59F-C
Zusammenfassung
We consider three general classes of data-driven statistical tests. Neyman's smooth tests, data-driven score tests and data-driven score tests for statistical inverse problems serve as important special examples for the classes of tests under consideration. Our tests are additionally incorporated with model selection rules. The rules are based on the penalization idea. Most of the optimal penalties, derived in statistical literature, can be used in our tests. We prove general consistency theorems for the tests from those classes. Our proofs make use of large deviations inequalities for deterministic and random quadratic forms. The paper shows that the tests can be applied for simple and composite parametric, semi- and nonparametric hypotheses. Applications to testing in statistical inverse problems and statistics for stochastic processes are also presented..