The Generalized Jackknife: Finite Samples and Subsample Sizes

Sharot, Trevor

doi:10.2307/2285332

Cited by 5 publications

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“…Comparison of( I 0), the expansion of the jackknifed estimator iJ, shows that 0and 0differ in a very minor way. Indeed Thorburn (1976) has shown that as n -+ 00, lim inf(var (O)/var(0))~I, which is the price paid for bias reduction. The operation of jackknifing alone will not induce asymptotic normality of (4).…”

Section: As In Hinkleymentioning

confidence: 99%

“…THE idea of splitting a sample of size ninto g groups ofsize heach in order to red uce bias, where one by one each group has a turn to be removed from the sample, was introduced by Quenouille (1949,1956). In what is to follow we will stay with the case n = g, h = I, although everything we do can be done equally for h » I; Sharot (1976) showed that in terms of mean squared error, h = I is the best choice. Let Y I , ... , Y n denote the sample, distributed according to a distribution function F that depends on an unknown parameter e. We wish to estimate or test £J; suppose 8( Y I , .. ·, Y n ) is such an estimate, and that 0_i is the estimate obtained by applying the estimation procedure to the sample with the ith random variable removed, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Transformations and the Jackknife

Cressie

1981

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Whether to jackknife a parameter estimate or some function of it has in the past relied on recommendations based on folklore rather than statistical analyses. This paper puts the jackknifed estimator into the context of finding a least squares estimator from a model involving a location parameter with additive “pseudo” errors. Obtaining and interpreting confidence intervals from the partitioning of the “total” sum of squares into “residual” sum of squares, plus a sum of squares due to a hypothesized value of the parameter, requires the error variance to be constant. This in turn can equally be interpreted as requiring the variance of the original estimator to be constant. Therefore, using this criterion of jackknifing “pivotal quantities”, it is possible in principle to find a prejackknifing transformation for any general problem.

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Section: As In Hinkleymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transformations and the Jackknife

Cressie

1981

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Finally, 0(2) may be theoretically less biased than other estimators; see Sharot (1976) for a comparison with 0(1). First, the infinitesimal jackknife is not a true jackknife in the sense that it is not based on reapplications of the original estimator t to subsamples of the data and thus its applicability may not be as wide as for the other jackknives.…”

Section: Discussionmentioning

confidence: 99%

Sharpening the Jackknife

Sharot¹

1976

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe jackknife is now well known as a widely applicable bias-reduction tool, with the added advantages of Tukey's variance estimator, and in certain applications, a gain in precision. In this paper a new family of jackknives is introduced, together with a variance estimator. The family includes the ordinary, first-order, and second-order jackknives as special cases and the variance estimator includes Tukey's as a special case. A sample-based decision rule for choosing a member of the family, intended to achieve a gain in precision over either order of jackknife, is given. The success of the rule is examined by simulation in estimation of the reciprocal of the parent mean and in ratio estimation.

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“…For this purpose, different levels of imbalance were applied to the data set which corresponded to 58 single cross hybrids. The cross-validation was performed by resampling a group of individuals using the generalized Jacknife procedure [ 23 ]. The generalized Jacknife method is based on dividing the sample data set C into g groups of equal size k , so that C = gk .…”

Section: Methodsmentioning

confidence: 99%

Prediction of Maize Single Cross Hybrids Using the Total Effects of Associated Markers Approach Assessed by Cross-Validation and Regional Trials

Melo

Pinho

Balestre

2014

The Scientific World Journal

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The present study aimed to predict the performance of maize hybrids and assess whether the total effects of associated markers (TEAM) method can correctly predict hybrids using cross-validation and regional trials. The training was performed in 7 locations of Southern Brazil during the 2010/11 harvest. The regional assays were conducted in 6 different South Brazilian locations during the 2011/12 harvest. In the training trial, 51 lines from different backgrounds were used to create 58 single cross hybrids. Seventy-nine microsatellite markers were used to genotype these 51 lines. In the cross-validation method the predictive accuracy ranged from 0.10 to 0.96, depending on the sample size. Furthermore, the accuracy was 0.30 when the values of hybrids that were not used in the training population (119) were predicted for the regional assays. Regarding selective loss, the TEAM method correctly predicted 50% of the hybrids selected in the regional assays. There was also loss in only 33% of cases; that is, only 33% of the materials predicted to be good in training trial were considered to be bad in regional assays. Our results show that the predictive validation of different crop conditions is possible, and the cross-validation results strikingly represented the field performance.

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The Generalized Jackknife: Finite Samples and Subsample Sizes

Cited by 5 publications

References 0 publications

Transformations and the Jackknife

Transformations and the Jackknife

Sharpening the Jackknife

Prediction of Maize Single Cross Hybrids Using the Total Effects of Associated Markers Approach Assessed by Cross-Validation and Regional Trials

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