The Annals of Statistics

Estimation of Quantiles in Certain Nonparametric Models

R.-D. Reiss

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Abstract

The deficiency of sample quantiles with respect to quasiquantiles is investigated under the assumption that the true density function has bounded derivatives. Then the sample quantile is still an efficient estimator of the true quantile but the relative deficiency of sample quantiles with respect to suitably defined quasiquantiles quickly tends to infinity for increasing sample sizes. If the second derivative of the true density function is bounded, then adaptive estimators will be found which are of a better performance than quasiquantiles. Corresponding results are derived for two-sided confidence intervals which are based on quasiquantiles and adaptive estimators.

Article information

Source
Ann. Statist., Volume 8, Number 1 (1980), 87-105.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344893

Digital Object Identifier
doi:10.1214/aos/1176344893

Mathematical Reviews number (MathSciNet)
MR557556

Zentralblatt MATH identifier
0424.62023

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions 62E20: Asymptotic distribution theory

Keywords
Adaptive estimators deficiency confidence intervals order statistics

Citation

Reiss, R.-D. Estimation of Quantiles in Certain Nonparametric Models. Ann. Statist. 8 (1980), no. 1, 87--105. doi:10.1214/aos/1176344893. https://projecteuclid.org/euclid.aos/1176344893


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