Yu P L, Lam K
Department of Statistics, University of Hong Kong.
Biometrics. 1997 Sep;53(3):1070-80.
Ranked set sampling (RSS) utilizes inexpensive auxiliary information about the ranking of the units in a sample to provide a more precise estimator of the population mean of the variable of interest Y, which is either difficult or expensive to measure. However, the ranking may not be perfect in most situations. In this paper, we assume that the ranking is done on the basis of a concomitant variable X. Regression-type RSS estimators of the population mean of Y will be proposed by utilizing this concomitant variable X in both the ranking process of the units 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 estimate for the population mean of X. It is found that when X and Y jointly follow a bivariate normal distribution, our proposed RSS regression estimator is more efficient than RSS and simple random sampling (SRS) naive estimators unless the correlation between X and Y is low (/rho/ < 0.4). Moreover, it is always superior to the regression estimator under SRS for all rho. When normality does not hold, this approach could still 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 suggested. An example of estimating the mean plutonium concentration in surface soil on the Nevada Test Site, Nevada, U.S.A., will be considered.
排序集抽样（RSS）利用关于样本中单元排序的廉价辅助信息，来提供对难以测量或测量成本高昂的目标变量Y的总体均值更精确的估计量。然而，在大多数情况下，排序可能并不完美。在本文中，我们假设排序是基于一个伴随变量X进行的。当X的总体均值已知时，通过在单元排序过程和估计过程中利用这个伴随变量X，将提出Y的总体均值的回归型RSS估计量。当X的均值未知时，将使用二重抽样来获得X的总体均值的估计。研究发现，当X和Y联合服从二元正态分布时，除非X和Y之间的相关性较低（/rho/ < 0.4），我们提出的RSS回归估计量比RSS和简单随机抽样（SRS）朴素估计量更有效。此外，对于所有的/rho/，它总是优于SRS下的回归估计量。当正态性不成立时，只要伴随变量X的分布形状仅略微偏离对称性，这种方法仍然可以表现得相当好。对于严重偏态的分布，将提出一种补救措施。将考虑一个估计美国内华达州内华达试验场表层土壤中钚平均浓度的例子。
