On Estimating a Population Proportion via Ranked Set Sampling

Abstract

SummaryThis paper explores the use of the rank set sampling (RSS) protocol as it pertains to the estimation of a population proportion. The maximum likelihood estimator (MLE) and the sample proportion, both based on the RSS data, are discussed and their corresponding asymptotic distributions are derived. Based on these results the MLE is found to be uniformly more efficient than the sample proportion. Nevertheless, both estimators are more efficient than the simple random sample proportion. The greatest gains in efficiency are obtained at the center of the parameter space. Finally, these results remain valid in the presence of judgment error.

Concomitant‐based rank set sampling proportion estimates

“…r 0 = r 1 = 0:9), the RSS estimate is more e cient than its SRS counterpart. We note that Terpstra [17] made a similar observation. However, the solution used in that paper was based on tedious sample space arguments that do not readily extend to the general k case.…”

Confidence intervals for a population proportion based on a ranked set sample

“…. , k. As discussed in Terpstra [9], Y i follows a B(n, π ki (p)) distribution, where π ki (p) = P [B(k, p) ≥ k − i + 1] and the B(n, p) notation denotes a binomial random variable with parameters n and p.…”

“…Much of this discussion has been paraphrased from Terpstra [9]. To begin, the joint sufficient statistics for p are given by Y = (Y 1 , Y 2 , .…”

“…More thorough discussions can be found in Terpstra [9] and/or Terpstra and Liudahl [11]. Basically, samples are acquired by randomly selecting k sets of k units, each from the (infinite) population of interest.…”

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.…”