Fast Estimators of the Jackknife

The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator will depend on the time required to compute itself. For some estimators the requ...

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Veröffentlicht in:The American statistician 1997-08, Vol.51 (3), p.235-240
1. Verfasser: Buzas, J. S.
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description The jackknife is a reliable method for estimating standard error nonparametrically. The method is easy to use, but is computationally intensive. The time required to compute the jackknife standard error for an estimator will depend on the time required to compute itself. For some estimators the required time is prohibitive. This may be especially true in simulation studies where and its standard error are computed for a large number of datasets. Let X 1 , X 2 , ..., X N be a random sample and the estimator computed with X i removed. Then is the jackknife estimator of the variability of where . In this paper estimators of are defined that can be computed quickly while sacrificing little precision or accuracy. The method requires that random variables are available that can be computed quickly and are strongly correlated with . It is described how can generally be obtained, and the method is illustrated with two examples. The paper focuses on the jackknife estimator for standard error, but the method can also be applied to quickly compute the jackknife estimator of bias.
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source Jstor Complete Legacy; Periodicals Index Online; JSTOR Mathematics & Statistics
subjects Approximation
Bootstrap
Cost estimates
Datasets
Estimate reliability
Estimation bias
Estimation methods
Estimators
Exact sciences and technology
Influence curve
Mathematics
Measurement error
Nonparametric inference
Probability and statistics
Random sampling
Sampling
Sampling theory, sample surveys
Sciences and techniques of general use
Standard error
Statistical variance
Statistics
title Fast Estimators of the Jackknife
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