The Annals of Statistics

Minimax linear estimation in a white noise problem

Linda H. Zhao

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Abstract

.Linear estimation of $f(x)$ at a point in a white noise model is considered. The exact linear minimax estimator of $f(0)$ is found for the family of $f(x)$ in which $f'(x)$ is Lip (M). The resulting estimator is then used to verify a conjecture of Sacks and Ylvisaker concerning the near optimality of the Epanechnikov kernel.

Article information

Source
Ann. Statist., Volume 25, Number 2 (1997), 745-755.

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031833671

Digital Object Identifier
doi:10.1214/aos/1031833671

Mathematical Reviews number (MathSciNet)
MR1439321

Zentralblatt MATH identifier
0879.62033

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 62C25: Compound decision problems

Keywords
White noise model density estimation linear minimax estimation Epanechnikov kernel

Citation

Zhao, Linda H. Minimax linear estimation in a white noise problem. Ann. Statist. 25 (1997), no. 2, 745--755. doi:10.1214/aos/1031833671. https://projecteuclid.org/euclid.aos/1031833671


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References

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  • PHILADELPHIA, PENNSy LVANIA 19104 E-MAIL: lzhao@stat.wharton.upenn.edu