REGRESSION ESTIMATOR IN RANKED SET SAMPLING

Ranked set sampling (RSS) utilizes inexpensive auxiliary information a bout the ranking of the units in a sample to provide a more precise es timator of the population mean of the variable of interest Y, which is either difficult or expensive to measure. However, the ranking may no t be perfect in most situations. In this paper, we assume that the ran king is done on the basis of a concomitant variable X. Regression-type RSS estimators of the population mean of Y will be proposed by utiliz ing this concomitant variable X in both the ranking process of the uni ts and the estimation process when the population mean of X is known. When X has unknown mean, double sampling will be used to obtain an est imate for the population mean of X. It is found that when X and Y join tly follow a bivariate normal distribution, our proposed RSS regressio n estimator is more efficient than RSS and simple random sampling (SRS ) naive estimators unless the correlation between X and Y is low (\p\ < 0.4). Moreover, it is always superior to the regression estimator un der SRS for all p. When normality does not hold, this approach could s till perform reasonably well as long as the shape of the distribution of the concomitant variable X is only slightly departed from symmetry. For heavily skewed distributions, a remedial measure will be suggeste d. An example of estimating the mean plutonium concentration in surfac e soil on the Nevada Test Site, Nevada, U.S.A., will be considered.