How to get central limit theorems for global errors of estimates.
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.
scientific article; zbMATH DE number 2165518
scientific article