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Estimation of bivariate characteristics using ranked set sampling
Authors:Mohammad Fraiwan Al-Saleh,&   Gang Zheng
Affiliation:Sultan Qaboos University and National Heart, Lung and Blood Institute
Abstract: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 Yu & Lam (1997) and Chen (2001). 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.
Keywords:bivariate ranked set sampling    regression estimator    relative efficiency    relative saving    simple random sampling
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