Summary
Letmn, p denote thep-th quantile based onn observations and let λp denote the population quantile. In this paper consistency of the bootstrap estimate of variance of\(\sqrt n (m_{n,p} - \lambda _p )\) is established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Babu, G. J. (1984). Bootstrapping statistics with linear combinations of chi-squares as weak limit,Sankhya, Series A,46, 85–93.
Babu, G. J. and Singh, K. (1978). On derviations between empirical and quantile processes for mixing random variables,J. Multivar. Anal.,8, 532–549.
Babu, G. J. and Singh, K. (1983). Inference on means using bootstrap,Ann. Statist.,11, 999–1003.
Babu, G. J. and Singh, K. (1984). Asymptotic representations related to jacknifing and bootstrappingL-statistics,Sankhya, Serie A,46, 195–206.
Babu, G. J. and Singh, K. (1984). On one term Edgeworth correction by Efron's bootstrap,Sankhya, Series A,46, 219–232.
Bickel, P. J. and Freedman, D. A. (1981). Some asymptotic theory for the bootstrap,Ann. Statist.,9, 1196–1217.
Efron, B. (1979). Bootstrap methods: Another look at the Jackknife,Ann. Statist.,7, 1–26.
Ghosh, M., Parr, W. C., Singh, K. and Babu, G. J. (1984). A note on bootstrapping the sample median,Ann. Statist.,12, 1130–1135.
Kiefer, J. (1967). On Bahadur's representation of sample quantiles,Ann. Math. Statist.,38, 1323–1342.
Singh, K. (1981). On the asymptotic accuracy of Efron's bootstrap,Ann. Statist.,9, 1187–1195.
Author information
Authors and Affiliations
About this article
Cite this article
Babu, G.J. A note on bootstrapping the variance of sample quantile. Ann Inst Stat Math 38, 439–443 (1986). https://doi.org/10.1007/BF02482530
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02482530