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A consistent goodness of fit test based on the total variation distance. (English) Zbl 0727.62053
Nonparametric functional estimation and related topics, NATO ASI Ser., Ser. C 335, 631-645 (1991).
Summary: [For the entire collection see Zbl 0722.00032.]
We propose a consistent test for testing a simple hypothesis versus a composite alternative. The simple hypothesis consists of a continuous distribution $$\nu$$, while the composite alternative is the set of probability measures $$\mu$$ such that $$\mu$$ is in total variation T($$\mu$$,$$\nu$$) at least distance $$\delta >0$$ away from $$\nu$$. For this hypothesis testing problem no uniformly consistent test exists. The proof of the consistency result implies a way to restrict the alternative in order to have uniform consistency, and thus uniform exponential consistency.

##### MSC:
 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference