SUMMARY. The jackknife. bootstrap and some other resampling plans are commonly used to estimate (and reduce) the bias and sampling error of statistical estimators. In these contexts. general (differentiable) statistical functionals crop up in a variety of models (especially. in nonparametric setups). A treatise of statistical functionals in resampling plans is considered along with a review of some of these recent developments.

Additional excerpts

Asymptotic theory of sequential shrunken estimation of statistical functionals

Functional approaches in resampling plans: A review of some recent developments

ABSTRACf In a nonparametric estimation problem. for a statistical functional. the risk (defined suitably) depends on n. the sample size. as well as F. the underlying distribution function. Sequential estimators based on appropriate stopping times possess the (first order) asymptotic minimum risk property. al though the picture is somewhat different for shrinkage versions of such sequential statistical functionals. In this context. the role of stopping times is explored in a systematic manner.

Asymptotic theory of sequential shrunken estimation of statistical functionals

Citations

Functional approaches in resampling plans: A review of some recent developments

STATISTICAL FUNCfIONAlS. STOPPING TIMES AND ASYMPTOTIC MINIMUM RISK PROPERTY

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