Abstract
We study for a finite d (≥ 1), the limit properties of the family of delete-d jackknife estimators of the variance of a sample quantile from a random sample of size n as n →∞. We consider central and intermediate sample quantiles and for the central case, we provide asymptotically unbiased delete-d jackknife estimators of its large-sample variance. In the intermediate case, the limit distribution of the delete-d jackknife estimator is free of d. For the sample median, the limit distributions of the delete-d jackknife estimators of its variance differ for sequences of odd and even values of n − d.
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Acknowledgements
The authors thank the reviewer for the helpful comments. H.N. Nagaraja would also like to express his gratitude to Professor Barry Arnold for being an inspiring teacher, a great mentor, a conscientious collaborator, and a wonderful friend.
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Nagaraja, H.N., Nagaraja, C.H. (2021). Large-Sample Properties of Jackknife Estimators of the Variance of a Sample Quantile. In: Ghosh, I., Balakrishnan, N., Ng, H.K.T. (eds) Advances in Statistics - Theory and Applications. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-62900-7_2
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