## The Annals of Statistics

### Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data

Xiaojing Xiang

#### 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.

#### Article information

Source
Ann. Statist., Volume 23, Number 3 (1995), 836-854.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324625

Digital Object Identifier
doi:10.1214/aos/1176324625

Mathematical Reviews number (MathSciNet)
MR1345203

Zentralblatt MATH identifier
0847.62025

JSTOR
links.jstor.org

#### Citation

Xiang, Xiaojing. Deficiency of the Sample Quantile Estimator with Respect to Kernel Quantile Estimators for Censored Data. Ann. Statist. 23 (1995), no. 3, 836--854. doi:10.1214/aos/1176324625. https://projecteuclid.org/euclid.aos/1176324625