Mathematical Methods of Statistics

, Volume 21, Issue 2, pp 93-108

First online:

Adaptive test on components of densities mixture

  • F. AutinAffiliated withLaborat. d’Anal., Topol., Probab., Aix-Marseille Univ. Email author 
  • , C. PouetAffiliated withLaborat. d’Anal, Topol., Probab., Ecole Centrale Marseille

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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.


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

2000 Mathematics Subject Classification

62G05 62G10 62G20