The Annals of Statistics

A note on nonparametric estimation of linear functionals

T. Tony Cai and Mark G. Low

Full-text: Open access

Abstract

Precise asymptotic descriptions of the minimax affine risks and bias-variance tradeoffs for estimating linear functionals are given for a broad class of moduli. The results are complemented by illustrative examples including one where it is possible to construct an estimator which is fully adaptive over a range of parameter spaces.

Article information

Source
Ann. Statist., Volume 31, Number 4 (2003), 1140-1153.

Dates
First available in Project Euclid: 31 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1059655908

Digital Object Identifier
doi:10.1214/aos/1059655908

Mathematical Reviews number (MathSciNet)
MR2001645

Zentralblatt MATH identifier
1105.62325

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures 62M99: None of the above, but in this section

Keywords
bias-variance tradeoffs density estimation modulus of continuity linear functionals nonparametric functional estimation nonparametric regression white noise model

Citation

Cai, T. Tony; Low, Mark G. A note on nonparametric estimation of linear functionals. Ann. Statist. 31 (2003), no. 4, 1140--1153. doi:10.1214/aos/1059655908. https://projecteuclid.org/euclid.aos/1059655908


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  • PHILADELPHIA, PENNSy LVANIA 19104-6340 E-MAIL: tcai@wharton.upenn.edu