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Regular version of the site

Article

Nonparametric density estimation from observations with multiplicative measurement errors

Annales de l’Institut Henri Poincaré. 2020. Vol. 56. No. 1. P. 36-67.

In this paper we study the problem of pointwise density es- timation from observations with multiplicative measurement errors. We elucidate the main feature of this problem: the influence of the estimation point on the estimation accuracy. In particular, we show that, depending on whether this point is separated away from zero or not, there are two different regimes in terms of the rates of convergence of the minimax risk. In both regimes we develop kernel–type density estimators and prove up- per bounds on their maximal risk over suitable nonparametric classes of densities. We show that the proposed estimators are rate–optimal by establishing matching lower bounds on the minimax risk. Finally we test our estimation procedures on simulated data.