Summary: The superiority of ranked set sampling (RSS) over simple random sampling (SRS) for estimating the mean of a population is well known. This paper introduces and investigates a bivariate version of RSS for estimating the means of two characteristics simultaneously. It turns out that this technique is always superior to SRS and the usual univariate RSS of the same size. The performance of this procedure for a specific distribution can be evaluated using simulation or numerical computation. For the bivariate normal distribution, the efficiency of the procedure with respect to that of SRS is evaluated exactly for set size \(m=2\) and 3.
The paper shows that the proposed estimator is more efficient than the regression RSS estimators proposed by P. Yu and K. Chen [Biometrics 53, No. 3, 1070-1080 (1997; Zbl 0896.62014)] and Z. Chen [J. Stat. Plann. Inference 92, 181-192 (2001; Zbl 0964.62009)]. Real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The procedure can be generalized to the case of multiple characteristics.