Adaptive test on components of densities mixture. (English) Zbl 1325.62095

Autin, F.; Pouet, C.

Math. Methods Stat. 21, No. 2, 93-108 (2012).

Summary: We are interested in testing whether two independent samples of \(n\) independent random variables are based on the same mixing-components or not. We provide a test procedure to detect if at least two mixing-components are distinct when their difference is a smooth function. Our test procedure is proved to be optimal according to the minimax adaptive setting that differs from the minimax setting by the fact that the smoothness is not known. Moreover, we show that the adaptive minimax rate suffers from a loss of order \((\sqrt{\log(\log (n))})^{-1}\) compared to the minimax rate.

MSC:

62G10	Nonparametric hypothesis testing
62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference

Keywords:

adaptation; Besov spaces; hypothesis testing; minimax theory; mixture models; nonparametric tests; wavelet decomposition

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