Goodness-of-fit testing strategies from indirect observations

Jean-Michel Loubes (1) , Clément Marteau (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider in this paper a goodness-of-fit testing problem in a density framework. In particular, we deal with an error-in-variables model where each new incoming observation is gathered with a random independent error. It is well known that in such a situation, we are faced with an inverse (deconvolution) problem. Nevertheless, following recent results in the Gaussian white noise model, we prove that using procedures containing a deconvolution step is not always necessary.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Michel Loubes, Clément Marteau. Goodness-of-fit testing strategies from indirect observations. Journal of Nonparametric Statistics, 2014, 26 (1), pp.85-99. ⟨hal-00949508⟩