Kernel estimators of an unknown multivariate regression function are investigated. A bandwidth-selection rule is considered, which can be formulated in terms of cross validation. Under mild assumptions on the kernel and the unknown regression function, it is seen that this rule is asymptotically optimal.
"Optimal Bandwidth Selection in Nonparametric Regression Function Estimation." Ann. Statist. 13 (4) 1465 - 1481, December, 1985. https://doi.org/10.1214/aos/1176349748