Ranked set sampling imputation methods in presence of correlated measurement errors

Abstract

Very little attention has been paid by the authors for providing improved imputation methods under correlated measurement errors (CMEs) using various sampling designs. This article addresses several power ratio imputation methods and the resulting estimators under ranked set sampling (RSS) when CMEs are present. The mean square error (MSE) is developed to assess how well the suggested estimators work under CMEs. The effectiveness of the proposed imputation methods and corresponding resultant estimators is assessed by a comprehensive simulation utilizing an artificially generated population. Further, an application of the proposed imputation methods is also provided using real data from Sweden’s municipalities consisting of the total number of seats in 1982 in municipal council taken as study variable and the number of conservative seats in 1982 in municipal council taken as auxiliary variable. The CMEs might arise due to common surveyor biases if the same surveyor collects information on both the “total number of seats in municipal council” and “the number of conservative seats in that municipal council”. The simulation and real data results show that the proposed power ratio imputation methods outperform the mean, conventional ratio, and product imputation methods.