I consider a method for combining different classifiers to develop more effective classification rules. The proposed combined classifier, which turns out to be strongly consistent, is quite simple to use in real applications. It is also shown that this combined classifier is, (strongly) asymptotically, at least as good as anyone of the individual classifiers. In addition, if one of the individual classifiers is already Bayes optimal (asymptotically), then so is the combined classifier.

Some results related to statistical classification in the presence of missing covariates are presented. We derive representations for the best (Bayes) classifier when some of the covariates can be missing; this is done without imposing any assumptions on the underlying missing probability mechanism. Furthermore, without assuming any missingness-at-random type of conditions, we also construct Bayes consistent classifiers that do not require any imputation-based techniques. Both parametric and non-parametric situations are considered but the emphasis is on the latter. In addition to simple missingness patterns, we also consider the full "Swiss cheese" model, where the missing covariates can be anywhere. Both mechanics and the theoretical validity of our results are discussed. Copyright 2007 Royal Statistical Society.

We investigate the construction of a BCa‐type bootstrap procedure for setting approximate prediction intervals for an efficient estimator θm of a scalar parameter θ, based on a future sample of size m. The results are also extended to nonparametric situations, which can be used to form bootstrap prediction intervals for a large class of statistics. These intervals are transformation‐respecting and range‐preserving. The asymptotic performance of our procedure is assessed by allowing both the past and future sample sizes to tend to infinity. The resulting intervals are then shown to be second‐order correct and second‐order accurate. These second‐order properties are established in terms of min(m, n), and not the past sample size n alone.

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