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How to get central limit theorems for global errors of estimates. (English) Zbl 1060.62056

The paper pays attention to global statistical errors in a nonparametric model with i.i.d.observations, such as the \(L_p\)-norm of differences, or information divergences, between estimates. The paper reviews the techniques leading to normal asymptotic laws for global errors, such as strong approximation and martingale theory of Poissonization. The preferences between these techniques usually depend on what estimator is taken into account. The author considers mainly the kernel and so-called Barron estimators. The latter are convex mixtures of the histogram and a priori given densities with the weights of the histogram tending to 1 as the sample size tends to infinity.
Reviewer: Igor Vajda (Praha)

MSC:

62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60F25 \(L^p\)-limit theorems
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References:

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