Nonparametric estimation of mean residual lifetime in ranked set sampling with a concomitant variable

Abstract

The mean residual lifetime (MRL) of a unit is its expected additional lifetime provided that it has survived until time t. The MRL estimation problem has been frequently addressed in the literature since it has wide applications in statistics, reliability and survival analysis. In this paper, we consider the problem of estimating the MRL in ranked set sampling when actual quantifications of a concomitant variable are available. To exploit the additional information of the concomitant variable, we introduce several MRL estimators based on some regression techniques. We then compare them with the standard MRL estimator in simple random sampling using Monte Carlo simulation and a real dataset from the Surveillance, Epidemiology, and End Results Program. Our results indicate the superiority of the procedures that we have developed when the quality of ranking is fairly good.

Keywords:

• Judgment ranking
• ranked set sampling
• relative efficiency
• Monte Carlo simulation
• nonparametric regression

Mathematics Subject Classifications (2020):

• 62D05
• 62G05

Acknowledgments

The authors thank the reviewers and an AE for helpful comments that have resulted in an improved paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data set utilized in this study is obtained from the Surveillance, Epidemiology and End Results (SEER) program of the US National Cancer Institute (NCI) (https://seer.cancer.gov/) with permission reference number 12395-Nov2017.

Additional information

Funding

Ehsan Zamanzade's research was carried out in IPM Isfahan branch and was in part supported by a grant from IPM, Iran (No. 1402620049).