Some Invariance Principles Relating to Jackknifing and Their Role in Sequential Analysis
TLDR
For a broad class of jackknife statistics, it was shown in this article that the Tukey estimator of the variance converges almost surely to its population counterpart, and that the usual invariance principles (relating to the Wiener process approximations) usually filter through jackknifing under no extra regularity conditions.Abstract:
For a broad class of jackknife statistics, it is shown that the Tukey estimator of the variance converges almost surely to its population counterpart. Moreover, the usual invariance principles (relating to the Wiener process approximations) usually filter through jackknifing under no extra regularity conditions. These results are then incorporated in providing a bounded-length (sequential) confidence interval and a preassigned-strength sequential test for a suitable parameter based on jackknife estimators.read more
Citations
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Sequential point estimation of estimable parameters based on u-statistics
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TL;DR: In this paper, an asymptotically risk-efficient sequential point estimation of regular functionals of distribution functions based on U-statistics is considered under appropriate regularity conditions.
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Restricted canonical correlations
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References
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Book ChapterDOI
On the asymptotic theory of fixed-width sequential confidence intervals for the mean.
TL;DR: In this article, a confidence interval of prescribed width 2d and prescribed coverage probability a for the unknown mean µ of the population is found for a sequence of independent observations from some population.
Journal ArticleDOI
Dependent Central Limit Theorems and Invariance Principles
TL;DR: In this article, central limit theorems for martingales and near-martingales without the existence of moments or the full Lindeberg condition were proved and extended to invariance principles with a discussion of random and nonrandom norming.