Open Access
September, 1984 A Note on Bootstrapping the Sample Median
Malay Ghosh, William C. Parr, Kesar Singh, G. Jogesh Babu
Ann. Statist. 12(3): 1130-1135 (September, 1984). DOI: 10.1214/aos/1176346731


Efron (1979, 1982), in his treatment of the bootstrap, discusses its use for estimation of the asymptotic variance of the sample median, in the sampling situation of independent and identically distributed random variables with common distribution function $F$ having a positive derivative continuous in a neighborhood of the true median $\mu$. The natural conjecture that the bootstrap variance estimator converges almost surely to the asymptotic variance is shown by an example to be false unless a tail condition is imposed on $F$. We prove that such strong convergence does hold under the fairly nonrestrictive condition that $E\lbrack\mid X^\alpha\rbrack < \infty$ for some $\alpha > 0$.


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Malay Ghosh. William C. Parr. Kesar Singh. G. Jogesh Babu. "A Note on Bootstrapping the Sample Median." Ann. Statist. 12 (3) 1130 - 1135, September, 1984.


Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0541.62010
MathSciNet: MR751302
Digital Object Identifier: 10.1214/aos/1176346731

Primary: 62E20
Secondary: 62G05

Keywords: bootstrap , median , standard error estimation

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • September, 1984
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