The Annals of Statistics

On Density Estimation in the View of Kolmogorov's Ideas in Approximation Theory

Rafael Hasminskii and Ildar Ibragimov

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 18, Number 3 (1990), 999-1010.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347736

Digital Object Identifier
doi:10.1214/aos/1176347736

Mathematical Reviews number (MathSciNet)
MR1062695

Zentralblatt MATH identifier
0705.62039

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation

Keywords
Nonparametric density estimation best approximation in $L_p$ norms Fano's inequality

Citation

Hasminskii, Rafael; Ibragimov, Ildar. On Density Estimation in the View of Kolmogorov's Ideas in Approximation Theory. Ann. Statist. 18 (1990), no. 3, 999--1010. doi:10.1214/aos/1176347736. https://projecteuclid.org/euclid.aos/1176347736


Export citation