Summary
We derive an asymptotic expansion of integrated square error in kernel-type nonparametric regression. A similar result is obtained for a cross-validatory estimate of integrated square error. Together these expansions show that cross-validation is asymptotically optimal in a certain sense.
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Hall, P. Asymptotic properties of integrated square error and cross-validation for kernel estimation of a regression function. Z. Wahrscheinlichkeitstheorie verw Gebiete 67, 175–196 (1984). https://doi.org/10.1007/BF00535267
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DOI: https://doi.org/10.1007/BF00535267