Leave-one-out cross-validation is a popular and readily implemented heuristic for bandwidth selection in nonparametric smoothing problems. In this note we elucidate the role of leave-one-out selection criteria by discussing a criterion introduced by Sarda (1993) for bandwidth selection for kernel distribution function estimators (KDFEs). We show that for this problem, use of the leave-one-out KDFE in the selection procedure is asymptotically equivalent to leaving none out. This contrasts with kernel density estimation, where use of the leave-one-out density estimator in the selection procedure is critical.Unfortunately, simulations show that neither method works in practice, even for samples of size as large as 1000. In fact, we show that for any fixed bandwidth, the expected value of the derivative of the leave-none-out criterion is asymptotically positive. This result and our simulations suggest that the criteria are increasing and that for sufficiently large samples (e.g., n = 100), the smallest available bandwidth will always be selected, thus contradicting the optimality result of Sarda for this estimator.As an alternative to minimizing a selection criterion, we propose a plug-in estimator of the asymptotically optimal bandwidth. Simulations suggest that the plug-in is a good esti-*Supported by Hatch Grant 151410 NYF tsupported by NSERC (Canada) and FCAR (Quebec) 1 mator of the asymptotically optimal bandwidth even for samples as small as 10 observations and is not too far from the finite sample optimal bandwidth.

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Item non‐response in sample surveys is usually addressed by imputation. A bootstrap method that treats the imputed values as if they were observed generally leads to variance estimates that are too small. Shao & Sitter (1996) introduced a bootstrap method in this context, which leads to consistent variance estimators when the sampling fraction is small. In the context of stratified simple random sampling, we introduce the independent bootstrap, which is valid even when the sampling fraction is large. It consists of modifying a bootstrap method for sample surveys, of independently generating the response status of each unit, and of imputing the non‐respondents in the bootstrap sample. We pay special attention to the bootstrap survey weights approach of Rao, Wu, & Yue (1992). The Canadian Journal of Statistics 42: 142–167; 2014 © 2014 Statistical Society of Canada