Dang Duc TrongNguyen Hoang ThanhNguyen Dang MinhNguyen Nhu Lan2022-10-132022-10-132021https://repository.vlu.edu.vn/handle/123456789/25310.1016/j.jspi.2021.04.002We consider the model Y = X + ξ where Y is observable, ξ is a noise random variable with density fξ , X has an unknown mixed density such that P(X = Xc ) = 1 − p, P(X = a) = p with Xc being continuous and p ∈ (0, 1), a ∈ R. Typically, in the last decade, the model has been widely considered in a number of papers for the case of fully known quantities a, fξ . In this paper, we relax the assumptions and consider the parametric error ξ ∼ σN(0, 1) with an unknown σ > 0. From i.i.d. copies Y1, . . . , Ym of Y we will estimate (σ, p, a, fXc ) where fXc is the density of Xc . We also find the lower bound of convergence rate and verify the minimax property of established estimators.en-USDeconvolutionMixture distributionInversion problemsNonparametric estimationjournal-article