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Biometrika 1985 72(2):481-484; doi:10.1093/biomet/72.2.481
© 1985 by Biometrika Trust
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MISEALLANEA

Asymptotic nonequivalence of some bandwidth selectors in nonparametric regression

W. HÄRDLE and J. S. MARRON

Fachbereich Mathematik, Johann Wolfgang Goethe Universität D-6000 Frankfurt am Main, Federal Republic of Germany
Department of Statistics, University of North Carolina Chapel Hill, N.C. 27514, U.S.A.

SUMMARY

The bandwidth selection problem in nonparametric kernel regression is considered. Bandwidth selectors based on cross-validation and on Akaike's information criterion, atc, and his finite prediction error, FBE, are among those compared. It is seen that they are not necessarily asymptotically equivalent. Conditions are given under which the equivalence holds and modifications are suggested which make the selectors equivalent.

Key Words: Bandwidth selection • Kernel estimator • Model selection • Nonparametric regression


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