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On density estimation in the view of Kolmogorov’s ideas in approximation theory. (English) Zbl 0705.62039
Summary: The paper deals with upper and lower bounds for the quality of (probability) density estimation. Connections are established between these problems and the theory of approximation of functions. Particularly, it is demonstrated how some of Kolmogorov’s concepts work.

MSC:
62G05 Nonparametric estimation
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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