The Annals of Statistics

Asymptotic nonequivalence of nonparametric experiments when the smoothness index is ½

Lawrence D. Brown and Cun-Hui Zhang

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Abstract

An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is ½

Article information

Source
Ann. Statist., Volume 26, Number 1 (1998), 279-287.

Dates
First available in Project Euclid: 28 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1030563986

Digital Object Identifier
doi:10.1214/aos/1030563986

Mathematical Reviews number (MathSciNet)
MR1611772

Zentralblatt MATH identifier
0932.62061

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 62M05: Markov processes: estimation

Keywords
Risk equivalence nonparametric regression density estimation white noise

Citation

Brown, Lawrence D.; Zhang, Cun-Hui. Asymptotic nonequivalence of nonparametric experiments when the smoothness index is ½. Ann. Statist. 26 (1998), no. 1, 279--287. doi:10.1214/aos/1030563986. https://projecteuclid.org/euclid.aos/1030563986


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References

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