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Some asymptotic results for jackknifing the sample quantile. (English) Zbl 0724.62049

Summary: This note studies the asymptotic behavior of the delete-d jackknife in the irregular case of a sample p-quantile, calculated from a sample of n iid r.v.’s.
Two results are obtained: (a) an almost sure rate of convergence of the delete-d jackknife histogram to the normal distribution; (b) almost sure convergence of the delete-d jackknife variance estimate to the asymptotic variance of the sample p-quantile.

MSC:

62G20 Asymptotic properties of nonparametric inference
62G09 Nonparametric statistical resampling methods
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