## The Annals of Probability

### Weak Convergence of Smoothed and Nonsmoothed Bootstrap Quantile Estimates

#### Abstract

Under fairly general assumptions on the underlying distribution function, the bootstrap process, pertaining to the sample $q$-quantile, converges weakly in $D_\mathbb{R}$ to the standard Brownian motion. Furthermore, weak convergence of a smoothed bootstrap quantile estimate is proved which entails that in this particular case the smoothed bootstrap estimate outperforms the nonsmoothed one.

#### Article information

Source
Ann. Probab. Volume 17, Number 1 (1989), 362-371.

Dates
First available in Project Euclid: 19 April 2007

http://projecteuclid.org/euclid.aop/1176991515

Digital Object Identifier
doi:10.1214/aop/1176991515

Mathematical Reviews number (MathSciNet)
MR972792

Zentralblatt MATH identifier
0684.62036

JSTOR