On the Effectiveness of the Takahasi's Ranked set Sample Estimator as Compared with the Regression Estimator

Abstract

SYNOPTIC ABSTRACTRanked set sampling (RSS) is a cost-effective sampling technique. Its two main formulations include McIntyre's RSS (MRSS) and Takahasi's RSS (TRSS) methods, which were proposed by McIntyre (1952) and Takahasi (1970) respectively. In this paper we compare the performances of the TRSS and its modified form (MTRSS) as suggested by Norris, Patii and Sinha (1995) for estimating a population mean as compared with the linear regression (LR) estimator with and without double sampling (DS). This investigation considers perfect as well as concomitant ranking scenarios while the main and the auxiliary variables follow jointly a bivariate normal distribution. Like the MRSS estimator (see Patii, Sinha and Taillie (1993)), the TRSS and TMRSS estimators show their better performances than the LR estimators with and without DS under perfect ranking scenario until a fairly high value of correlation between the main and the auxiliary variables. Even under the concomitant ranking situation the performance of the RSS estimators is quite encouraging. However, the MTRSS method appears to be more attractive and useful than the MRSS and the TRSS methods for conducting a survey sampling where the quantification of a unit could be enormously high. An example based on a real data set is presented to illustrate the methods.