The Annals of Statistics

Asymptotic Normality of the Kernel Quantile Estimator

Michael Falk

Full-text: Open access

Abstract

Multidimensional asymptotic normality of the kernel quantile estimator is established under fairly general conditions on the underlying distribution function and on the kernel. Sharpening these assumptions, one can utilize the proof to achieve also a bound for the rate of convergence which entails the comparison of the kernel estimator with the empirical quantile on the basis of their covering probabilities.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 428-433.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346605

Digital Object Identifier
doi:10.1214/aos/1176346605

Mathematical Reviews number (MathSciNet)
MR773180

Zentralblatt MATH identifier
0567.62035

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62G05: Estimation 62G20: Asymptotic properties

Keywords
Kernel estimator empirical quantile central limit theorem covering probability

Citation

Falk, Michael. Asymptotic Normality of the Kernel Quantile Estimator. Ann. Statist. 13 (1985), no. 1, 428--433. doi:10.1214/aos/1176346605. https://projecteuclid.org/euclid.aos/1176346605


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