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Biometrika 1990 77(2):415-419; doi:10.1093/biomet/77.2.415
© 1990 by Biometrika Trust
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MISCELLANEA

On variance estimation in nonparametric regression

PETER HALL and J. S. MARRON

Department of Statistics, Australian National University Canberra, ACT2601, Australia
Department of Statistics, University of North Carolina Chapel Hill, NC27514, U.S.A.

A simple explicit estimator of variance in nonparametric regression is suggested, based on the mean square of a sequence of residuals. The estimator is valid for general error distributions, has elementary bias and variance properties, and is optimal to both first and second orders.

Key Words: Curve estimation • Kernel estimator • Nonparametric regression • Residual • Smoothing • Variance estimation


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