Statistics and Its Interface

Volume 14 (2021)

Number 2

Estimating equation estimators of quantile differences for one sample with length-biased and right-censored data

Pages: 183 – 195

DOI: https://dx.doi.org/10.4310/20-SII626

Authors

Li Xun (School of Mathematics and Statistics, Changchun University of Technology)

Guangchao Zhang (School of Mathematics and Statistics, Changchun University of Technology)

Dehui Wang (School of Mathematics, Jilin University)

Yong Zhou (School of Statistics and Management, Shanghai University of finance and Economics)

Abstract

This paper estimates quantile differences for one sample with length-biased and right-censored (LBRC) data. To ensure the asymptotic unbiasedness of the estimator, the estimating equation method is adopted. To improve the efficiency of the estimator, in the sense of having a lower mean squared error, the kernel-smoothed approach is employed. To make full use of the features of LBRC data, the augmented inverse probability complete case weight is investigated in detail. Moreover, the consistency and asymptotic normality of the proposed estimators are established. The numerical simulations are conducted to examine the performance of the estimators.

Keywords

quantile difference, length bias, informative censoring, estimating equation, kernel function

Full Text (PDF format)

Xun’s work is partially supported by National Natural Science Foundation of China (11701043), Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period (JJKH20191299KJ), and Scholarship from China Scholarship Council (201808220176). Wang’s work is supported by National Natural Science Foundation of China (No. 11871028, 11731015, 11571051, 11501241), Natural Science Foundation of Jilin Province (No. 20180101216JC, 20170101057JC, 20150520053JH), and Program for Changbaishan Scholars of Jilin Province (2015010). Zhou’s work is supported by the State Key Program of National Natural Science Foundation of China (71331006, 71931004), the State Key Program in the Major Research Plan of National Natural Science Foundation of China (91546202).

Received 28 July 2018

Accepted 1 July 2020

Published 22 December 2020