Golubev, G. K. Nonparametric estimation of smooth probability densities in \(L_ 2\). (English. Russian original) Zbl 0785.62039 Probl. Inf. Transm. 28, No. 1, 44-54 (1992); translation from Probl. Peredachi Inf. 28, No. 1, 52-62 (1992). Let \(x_ 1,x_ 2,\dots,x_ n\) be a sequence of i.i.d. r.v., having unknown density \(p(x)\), \(x \in \mathbb{R}\). The author constructs asymptotically minimax estimators of \(p(x)\) based on the sample \(x_ 1,\dots,x_ n\). The quality of the estimation is measured by a quadratic risk function. A priori information on the smoothness of \(p(x)\) is absent. Reviewer: M.A.Mirzakhmedov (Tashkent) Cited in 18 Documents MSC: 62G07 Density estimation 62C20 Minimax procedures in statistical decision theory Keywords:\(L2\)-densities; asymptotically minimax estimators; quadratic risk function PDFBibTeX XMLCite \textit{G. K. Golubev}, Probl. Inf. Transm. 28, No. 1, 44--54 (1992; Zbl 0785.62039); translation from Probl. Peredachi Inf. 28, No. 1, 52--62 (1992)