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Biometrika 1990 77(2):377-381; doi:10.1093/biomet/77.2.377
© 1990 by Biometrika Trust
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The choice of weights in kernel regression estimation

THEO GASSER and JOACHIM ENGEL

Zentralinstitut für Seelische Gesundheit J5, P.O.B. 5970, 6800 Mannheim 1, Federal Republic of Germany
Institut für Angewandte Mathematik, Universität Heidelberg Im Neuenheimer Feld 294, 6900 Heidelberg, Federal Republic of Germany

For kernel regression estimation a weighting scheme due to Nadaraya and Watson has been associated with random design, and a convolution type weighting scheme with fixed design. Based on integrated mean square error, none of the estimators is uniformly optimal in either design. However, the convolution type weights are minimax optimal. Further advantages of this estimator can be seen in the structure of the bias.

Key Words: Fixed design • Kernel estimator • Minimax optimality • Nonparametric regression • Random design


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