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Adaptive goodness-of-fit testing from indirect observations

Cristina ButuceaCatherine MatiasChristophe Pouet — 2009

Annales de l'I.H.P. Probabilités et statistiques

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density and some known noise density . We assume that is polynomially smooth. We provide goodness-of-fit testing procedures for the test : = , where the alternative is expressed with respect to 𝕃 2 -norm (i.e. has the form ψ n - 2 f - f 0 2 2 𝒞 ). Our procedure is adaptive with respect to the unknown smoothness parameter of . Different testing rates ( ...

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