## The Annals of Statistics

### Relative Deficiency of Kernel Type Estimators of Quantiles

Michael Falk

#### 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

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