Multiple observers ranked set samples for shrinkage estimators

Abstract

Ranked set sampling (RSS) is used as a powerful data collection technique for situations where measuring the study variable requires a costly and/or tedious process while the sampling units can be ranked easily (e.g. osteoporosis research). In this paper, we develop ridge and Liu-type shrinkage estimators under RSS data from multiple observers to handle the collinearity problem in estimating coefficients of linear regression, stochastic restricted regression and logistic regression. Through extensive numerical studies, we show that shrinkage methods with the multi-observer RSS result in more efficient coefficient estimates. The developed methods are finally applied to bone mineral data for analysis of bone disorder status of women aged 50 and older.

Keywords:

• Ranked set sampling
• multiple observer
• collinearity
• ridge estimator
• stochastic restricted regression
• logistic regression

Acknowledgements

The authors would like to thank the editor, the associate editor and three anonymous referees for their constructive comments which improved the quality and presentation of the paper.

Disclosure statement

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

Additional information

Funding

Armin Hatefi acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).