A consistent goodness of fit test based on the total variation distance. (English) Zbl 0727.62053

Györfi, László; Van der Meulen, Edward C.

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

Keywords:

consistent test; simple hypothesis; composite alternative; consistency; uniform consistency; uniform exponential consistency