Median ranked set sampling with concomitant variables and a comparison with ranked set sampling and regression estimators

Abstract

Ranked set sampling (RSS), as suggested by McIntyre (1952), assumes perfect ranking, i.e. without errors in ranking, but for most practical applications it is not easy to rank the units without errors in ranking. As pointed out by Dell and Clutter (1972) there will be a loss in precision due to the errors in ranking the units. To reduce the errors in ranking, Muttlak (1997) suggested using the median ranked set sampling (MRSS). In this study, the MRSS is used to estimate the population mean of a variable of interest when ranking is based on a concomitant variable. The regression estimator uses an auxiliary variable to estimate the population mean of the variable of interest. When one compares the performance of the MRSS estimator to RSS and regression estimators, it turns out that the use of MRSS is more efficient, i.e. gives results with smaller variance than RSS, for all the cases considered. Also the use of MRSS gives much better results in terms of the relative precision compared to the regression estimator for most cases considered in this study unless the correlation between the variable of interest and the auxiliary is more than 90 per cent. © 1998 John Wiley & Sons, Ltd.