Estimation of convolution in the model with noise

Estimation of a fold convolution in additive noise model with compactly supported noise density

“…Under some regular conditions for the density f of X, we derive a convergence rate of the estimator. We also have shown that the estimator attains the same rate as the one of Chesneau et al [15] if the density g is supersmooth. A possible extension of this work is to study our estimation procedure in the case of unknown noise density g. We leave this problem for our future research.…”

“…For 1 m  , the problem of estimating m f reduces to the density deconvolution problem. To the best of our knowledge, for ,2 mm   , so far this problem has been only studied by Chesneau et al [15]. In that paper, the authors constructed a kernel type of estimator for m f under the assumption that ft g is nonvanishing on , where the function     ft itx g t f x e dt  …”

“…For I TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 21, SỐ T1-2018 CHUYÊN SAN KHOA HỌC TỰ NHIÊN, TẬP 2, SỐ 1, 2018 77 instance, the case in which g is a uniform density or a compactly supported density in general. In the present paper, as a continuation of the paper of Chesneau et al [15], we consider the case of compactly supported noise density g . In fact, the problem was studied by Trong-Phuong [16] in the case of 1 m  ; however, the problem has more challenge with ,2   mm .…”