The Annals of Statistics

Relative Deficiency of Kernel Type Estimators of Quantiles

Michael Falk

Full-text: Open access

Abstract

In this paper the asymptotic relative deficiency of the sample $q$-quantile with respect to kernel type estimators of the $q$-quantile is evaluated. The comparison is based on the mean square errors of the estimators. The result suggests a purely analytic measure of performance within the class of kernels. It is notable that a similar situation occurs when kernel estimators of a distribution function are studied.

Article information

Source
Ann. Statist., Volume 12, Number 1 (1984), 261-268.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346405

Digital Object Identifier
doi:10.1214/aos/1176346405

Mathematical Reviews number (MathSciNet)
MR733512

Zentralblatt MATH identifier
0533.62040

JSTOR
links.jstor.org

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

Keywords
Sample $q$-quantile kernel estimator mean square error deficiency Bahadur approximation

Citation

Falk, Michael. Relative Deficiency of Kernel Type Estimators of Quantiles. Ann. Statist. 12 (1984), no. 1, 261--268. doi:10.1214/aos/1176346405. https://projecteuclid.org/euclid.aos/1176346405


Export citation