The Annals of Statistics

Bias-Variance Tradeoffs in Functional Estimation Problems

Mark G. Low

Full-text: Open access

Abstract

It is shown in infinite-dimensional Gaussian problems that affine estimators minimax the variance among all estimators of a linear functional subject to a constraint on the bias. Likewise, affine estimators also minimax the square of the bias among all estimates of a linear functional subject to a constraint on the variance.

Article information

Source
Ann. Statist., Volume 23, Number 3 (1995), 824-835.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324624

Digital Object Identifier
doi:10.1214/aos/1176324624

Mathematical Reviews number (MathSciNet)
MR1345202

Zentralblatt MATH identifier
0838.62006

JSTOR
links.jstor.org

Subjects
Primary: 62C05: General considerations
Secondary: 62E20: Asymptotic distribution theory 62J02: General nonlinear regression 62G05: Estimation 62M99: None of the above, but in this section

Keywords
Bias-variance tradeoff Cramer-Rao inequality minimax risk white noise model modulus of continuity

Citation

Low, Mark G. Bias-Variance Tradeoffs in Functional Estimation Problems. Ann. Statist. 23 (1995), no. 3, 824--835. doi:10.1214/aos/1176324624. https://projecteuclid.org/euclid.aos/1176324624


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