Ranked Set Sampling: Its Relevance and Impact on Statistical Inference

Abstract

Ranked set sampling RSS is an approach to data collection and analysis that continues to stimulate substantial methodological research. It has spawned a number of related methodologies that are active research arenas as well, and it is finally beginning to find its way into significant applications beyond its initial agricultural-based birth in the seminal paper by McIntyre 1952. In this paper, we provide an introduction to the basic concepts underlying ranked set sampling, in general, with specific illustrations from the one-and two-sample settings. Emphasis is on the breadth of the ranked set sampling approach, with targeted discussion of the many options available to the researcher within the RSS paradigm. The paper also provides a thorough bibliography of the current state of the field and introduces the reader to some of the most promising new methodological extensions of the RSS approach to statistical data analysis.

Bayesian nonparametric models for ranked set sampling

“…Much of the current RSS literature is dominated by stringent attachment to design assumptions, from balanced RSS to unbalanced RSS and beyond. (See, for example, the annotated bibliography by Kaur et al (1995), and the recent survey paper by Wolfe (2012)). In light of the likelihood principle, the role of RSS as a design is altered: its task is solely to deliver the data (and the likelihood).…”

Bayesian Estimation of Measles Vaccination Coverage Under Ranked Set Sampling

“…For a binary population the success probability p can be viewed as a proportion of individuals possessing certain known characteristic in the population. In classical inference on a population proportion, the ranked set sampling with binary data has already been introduced and used by many researchers like, among others, Lacayo et al (2002), Kvam (2003), Terpstra (2004), Terpstra andLiudahl (2004), Chen et al (2005Chen et al ( , 2006Chen et al ( , 2007Chen et al ( , 2009), Terpstra and Nelson (2005), Terpstra and Miller (2006), Chen (2008), Gemayel etal.,(2012 used RSS for auditing purpose, Wolfe (2010Wolfe ( , 2012 and discussed application of RSS to air quality monitoring. Mirkamali (2010, 2011) used ranked set sample for binary data in the context of control charts for attributes.…”

Linear Penalized Spline Model Estimation Using Ranked Set Sampling Technique

“…A classical sampling method to fit spline models considers Simple Random Sampling (SRS) when selecting units. However, since it is practically more efficient, Ranked Set Sampling (RSS) has an increasing popularity when estimating regression models, [23]. This is because it can minimize sampling costs and furthermore, it can improve efficiency of the estimated parameters in the underlying model, [22].…”

“…They proved that the estimated mean using RSS method is an unbiased estimator to the population mean as well as has less variance than usual SRS estimated mean. The recent monograph by [23] summarized all research linked to RSS method until that date. He presented the dramatic increase of using RSS method in different statistical fields (e.g.…”