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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.

MSC:

62G07 Density estimation
62C20 Minimax procedures in statistical decision theory
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