Varied L Ranked Set Sampling Scheme

Abstract

In this article, we propose a generalized ranked set sampling (RSS) scheme, namely, varied L-RSS (VLRSS), for estimating the population mean. The VLRSS scheme encompasses several existing RSS schemes and helps in selecting more representative samples from the target population. It is shown that for a symmetric population, the mean estimator under VLRSS scheme is unbiased, and with reasonable assumptions, it is considerably better than the mean estimators based on RSS and LRSS schemes. Moreover, we also study the effect of imperfect ranking on the performance of VLRSS-based mean estimator. It turns out that, under an imperfect VLRSS scheme, the proposed estimator outperforms its counterparts. The proposed scheme is also illustrated with a case study using a real data set.

AMS Subject Classification:

• 62D05

Keywords:

• Mean squared error
• Perfect and imperfect rankings
• Ranked set sampling
• Relative efficiency
• Unbiased estimator

Acknowledgments

The authors are thankful to the editor-in-chief, associate editor, and three reviewers for their valuable comments and suggestions that greatly improved the article.