Consistent density deconvolution under partially known error distribution

Maik Schwarz , Sébastien van Bellegem

We estimate the distribution of a real-valued random variable from contaminated observations. The additive error is supposed to be normally distributed, but with unknown variance. The distribution is identifiable from the observations if we restrict the class of considered distributions by a simple condition in the time domain. A minimum distance estimator is shown to be consistent imposing only a slightly stronger assumption than the identification condition.

Mots clés: primary; secondary

Maik Schwarz, Sébastien van Bellegem. Consistent density deconvolution under partially known error distribution. Statistics and Probability Letters, 2009, 80 (3-4), pp.236. ⟨10.1016/j.spl.2009.10.012⟩. ⟨hal-00602314⟩