Relative precision of ranked set sampling: A comparison with the regression estimator

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AbstractRanked set sampling (RSS) utilizes inexpensive auxiliary information about the magnitude of the variable of interest in order to rank randomly drawn sampling units before quantifying a selected subset of these units. The units to be quantified are chosen, on the basis of the ranking information, in a way that makes the RSS estimator of the population mean at least as efficient as the simple random sample estimator with the same number of quantifications. The RSS protocol does not prescribe or restrict the nature of the outside information that is used for ranking the units; however, a common method is on the basis of an auxiliary variable and, here it is natural to ask how the RSS estimator compares with the regression estimator. This paper compares the performance of the two estimators in four situations depending on whether the ranking is perfect or is on the basis of the auxiliary variable and depending on whether double sampling is or is not used for the regression estimator. With perfect ranking, we find that the RSS estimator is considerably more efficient than the regression estimator unless the correlation between the main variable and the auxiliary variable is quite high (say, |ρ| > 0.85). When the ranking is on the basis of the auxiliary variable, the performance of the two methods is comparable for low correlation (say,|ρ| < 0.85), but the regression estimator is more efficient at higher correlations. The investigation assumes that the main and auxiliary variables jointly follow a bivariate normal distribution; this model is considered to be favourable to the regression estimator since the latter is unbiased under bivariate normality, while the RSS estimator is always unbiased.