The Annals of Statistics

Minimax linear estimation in a white noise problem

Linda H. Zhao

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.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

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

First available in Project Euclid: 12 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

White noise model density estimation linear minimax estimation Epanechnikov kernel


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

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