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Biometrika 1991 78(2):436-441; doi:10.1093/biomet/78.2.436
© 1991 by Biometrika Trust
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MISCELLANEA

The effect of discretization error on bandwidth selection for kernel density estimation

SHEAN-TSONG CHIU

Department of Statistics, Colorado State University Fort Collins, Colorado 80523, U.S.A.

It is well known that the cross-validation score function of discretized data often tends to -{infty} as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions, it is shown that the bandwidth selected by the proposed procedure is asymptotically equivalent to the bandwidth selected by cross-validation of the original unrounded data. The advantages of the proposed procedure are demonstrated in two examples.

Key Words: Bandwidth selection • Characteristic function • Cross-validation • Discretization effect • Kernel density estimat


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