The Annals of Statistics

On Trigonometric Series Estimates of Densities

Peter Hall

Full-text: Open access

Abstract

It is pointed out that several results due to Walter and Blum do not hold strictly as they are stated. We find expansions for the mean square errors and mean integrated square errors of trigonometric series estimates of densities, and use them to compare the efficiencies of the estimates.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 683-685.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345474

Digital Object Identifier
doi:10.1214/aos/1176345474

Mathematical Reviews number (MathSciNet)
MR615446

Zentralblatt MATH identifier
0484.62057

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation

Keywords
Density estimate Dirichlet kernel Fejer kernel Fourier series mean square error

Citation

Hall, Peter. On Trigonometric Series Estimates of Densities. Ann. Statist. 9 (1981), no. 3, 683--685. doi:10.1214/aos/1176345474. https://projecteuclid.org/euclid.aos/1176345474


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