Theory & Methods: Estimation of bivariate characteristics using ranked set sampling

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) andChen (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.

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

“…The extension of the the RSS protocol of Kaur et al (1997) is also compared to the two specific RSS protocols for the simultaneous estimation of the mean of two or more characteristics proposed by Al-Saleh and Zheng (2002) and by Ridout (2003).…”

“…Several other authors have considered estimating multiple characteristics. Al-Saleh and Zheng (2002) introduce a bivariate version of balanced RSS for estimating the mean of bivariate characteristics simultaneously and Ridout (2003) proposes a method that seeks to achieve sample that are nearly balanced with respect to the ranks of all the study variables. Norris et al (1995) use a real data set to examine the efficiencies of some RSS methods for estimating the means of multiple characteristics in a single investigation.…”

The matched pair sign test using bivariate ranked set sampling for different ranking based schemes

“…Estimation of bivariate characteristics using bivariate ranked set sampling (BVRSS) was introduced first by [24]. Later, in similar manner, [25] introduced two-layer ranked set sampling with concomitant variables.…”

“…They indicated that this BVRSS procedure can be easily extended to multivariate RSS. Based on [24], a BVRSS can be obtained as follows:…”

Ranked set sampling: its essence and some new applications

“…The Fisher information theory of RSS has been established, see Chen (2000a) and Bai and Chen (2003). A host of new RSS schemes such as the adaptive RSS and multi-layer RSS using either variables of interest or concomitant variables have been devised, see Al-Saleh and Zheng (2002), Chen (2002) and Chen and Shen (2003). Optimal RSS designs have been developed for various problems such as estimation of parameters in parametric families, estimation of quantiles and distribution-free tests, see Chen and Bai (2000), Chen (2001) and Ozturk andWolfe (2000a, b, c, 2001).…”