Best linear unbiased and invariant estimation in location-scale families based on double-ranked set sampling

Abstract

In this article, we propose the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the unknown parameters of location-scale family of distributions based on double-ranked set sampling (DRSS) using perfect and imperfect rankings. These estimators are then compared with the BLUEs and BLIEs based on ranked set sampling (RSS). It is shown that under perfect ranking, the proposed estimators are uniformly better than the BLUEs and BLIEs obtained via RSS. We also propose the best linear unbiased quantile (BLUQ) and the best linear invariant quantile (BLIQ) estimators for normal distribution under DRSS. It is observed that the proposed quantile estimators are more efficient than the BLUQ and BLIQ estimators based on RSS for both perfect and imperfect orderings.

Keywords:

• Best linear invariant estimator
• Best linear unbiased estimator
• Double-ranked set sampling
• Location and scale parameters
• Mean squared error
• Perfect and imperfect ranking
• Ranked set sampling
• Relative efficiency

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05
• 62F10

Acknowledgment

The authors are thankful to the associate editor and two anonymous referees for their helpful suggestions and comments that significantly improved the current version of the manuscript.