Translator Disclaimer
June, 1995 Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data
Xiaojing Xiang
Ann. Statist. 23(3): 836-854 (June, 1995). DOI: 10.1214/aos/1176324625

Abstract

Consider a statistical procedure (Method A) which is based on $n$ observations and a less effective procedure (Method B) which requires a larger number $k_n$ of observations to give equal performance under a certain criterion. To compare two different procedures, Hodges and Lehmann suggested that the difference $k_n - n$, called the deficiency of Method B with respect to Method A, is the most natural quantity to examine. In this article, the performance of two kernel quantile estimators is examined versus the sample quantile estimator under the criterion of equal covering probability for randomly right-censored data. We shall show that the deficiency of the sample quantile estimator with respect to the kernel quantile estimators is convergent in infinity with the maximum rate when the bandwidth is chosen to be optimal. A Monte Carlo study is performed, along with an illustration on a real data set.

Citation

Download Citation

Xiaojing Xiang. "Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data." Ann. Statist. 23 (3) 836 - 854, June, 1995. https://doi.org/10.1214/aos/1176324625

Information

Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0847.62025
MathSciNet: MR1345203
Digital Object Identifier: 10.1214/aos/1176324625

Subjects:
Primary: 62F12
Secondary: 62G05, 62G20, 62G30

Rights: Copyright © 1995 Institute of Mathematical Statistics

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.23 • No. 3 • June, 1995
Back to Top