The Annals of Statistics

Superefficiency in nonparametric function estimation

Lawrence D. Brown, Mark G. Low, and Linda H. Zhao

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Fixed parameter asymptotic statements are often used in the context of nonparametric curve estimation problems (e.g., nonparametric density or regression estimation). In this context several forms of superefficiency can occur. In contrast to what can happen in regular parametric problems, here every parameter point (e.g., unknown density or regression function) can be a point of superefficiency.

We begin with an example which shows how fixed parameter asymptotic statements have often appeared in the study of adaptive kernel estimators, and how superefficiency can occur in this context. We then carry out a more systematic study of such fixed parameter statements. It is shown in four general settings how the degree of superefficiency attainable depends on the structural assumptions in each case.

Article information

Ann. Statist. Volume 25, Number 6 (1997), 2607-2625.

First available in Project Euclid: 30 August 2002

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Mathematical Reviews number (MathSciNet)

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Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties 62B15: Theory of statistical experiments 62M05: Markov processes: estimation

Superefficiency nonparametric function estimation asymptotics


Brown, Lawrence D.; Low, Mark G.; Zhao, Linda H. Superefficiency in nonparametric function estimation. Ann. Statist. 25 (1997), no. 6, 2607--2625. doi:10.1214/aos/1030741087.

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