Finite population corrections for ranked set sampling

Patil, G. P.; Sinha, Arun K.; Taillie, C.

doi:10.1007/bf01856537

Cited by 46 publications

(35 citation statements)

References 3 publications

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“…They showed that the RSS estimator of the population mean is unbiased and they derived an explicit formula for its variance when the set size is k = 2 and the underlying population has a discrete uniform distribution. Patil et al (1995) extended this result to more general finite populations and to larger set sizes. Takahasi and Futatsuya (1998) showed that, when samples are drawn without replacement, the relative precision of the RSS estimator of the population mean relative to the SRS estimator with the same number of units quantified, is bounded above by 1.…”

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confidence: 79%

Design based estimation for ranked set sampling in finite populations

Jozani

Johnson

2010

Environ Ecol Stat

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In this paper, we consider design-based estimation using ranked set sampling (RSS) in finite populations. We first derive the first and second-order inclusion probabilities for an RSS design and present two Horvitz-Thompson type estimators using these inclusion probabilities. We also develop an alternate Hansen-Hurwitz type estimator and investigate its properties. In particular, we show that this alternate estimator always outperforms the usual Hansen-Hurwitz type estimator in the simple random sampling with replacement design with comparable sample size. We also develop formulae for ratio estimator for all three developed estimators. The theoretical results are augmented by numerical and simulation studies as well as a case study using a well known data set. These show that RSS design can yield a substantial improvement in efficiency over the usual simple random sampling design in finite populations.

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confidence: 79%

Design based estimation for ranked set sampling in finite populations

Jozani

Johnson

2010

Environ Ecol Stat

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“…However, we are awaiting appropriate data collected using ranked set sampling, and future work will apply the RSBLUQE to real-data assessments for newly proposed statistically verifiable ideal standards. We also propose to consider using the RSBLUQE in finite population applications, perhaps for the picking of observations from a finite group of air quality monitoring stations, and we hope to develop the necessary theory for this (following Patil et al, 1995). Finally, we propose to consider how we might extend the RSBLUQE theory for non-normal populations commonly used in environmental investigations.…”

Section: Best Linear Unbiased Quantile Estimation With Ranked Set Sammentioning

confidence: 95%

Best linear unbiased quantile estimators for environmental standards

Barnett

Bown

2002

Environmetrics

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SUMMARYRecent research has sought to develop a statistically based approach to setting environmental standards, prompted by Barnett and O'Hagan (1997) whose recommendations for a statistically verifiable ideal standard (SVIS) were endorsed by the Royal Commission on Environmental Pollution (1998). Many current environmental standards are set without due consideration of uncertainty and variation and are often based on poorly defined principles. In this article we propose an SVIS set on a population quantile where inferences about that quantile are achieved through best linear unbiased quantile estimation (BLUQE). We concentrate on estimation using small samples from the normal distribution with both parameters unknown, as is often the case in environmental problems. We investigate the efficiency of this estimator in comparison with a quantile estimator based upon the common sample estimators of mean and standard deviation, X and S, respectively. From extensive simulation, we tabulate 5 per cent and 1 per cent critical values for the 0.95 and 0.99 BLUQE and develop an approximate significance testing procedure, which we demonstrate using river water quality data. We consider the difference in power between this approximate test and a coefficient of variation-based approach appealing to properties of the non-central t distribution. Finally, we examine ranked set sampling and compare best linear unbiased quantile estimation based on ranked set samples with that based on ordinary random samples, demonstrating impressive efficiency gains.

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“…Table 1 represents the structure of RSS. For more details about RSS (Jozani and Johnson, 2011;Kowalczyk, 2004;Patil et al, 1995;Takahasi and Futatsuya, 1998).…”

Section: Ranked Set Sampling Proceduresmentioning

confidence: 99%

On inference of multivariate means under ranked set sampling

Rochani

Linder

Samawi

et al. 2018

CSAM

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In many studies, a researcher attempts to describe a population where units are measured for multiple outcomes, or responses. In this paper, we present an efficient procedure based on ranked set sampling to estimate and perform hypothesis testing on a multivariate mean. The method is based on ranking on an auxiliary covariate, which is assumed to be correlated with the multivariate response, in order to improve the efficiency of the estimation. We showed that the proposed estimators developed under this sampling scheme are unbiased, have smaller variance in the multivariate sense, and are asymptotically Gaussian. We also demonstrated that the efficiency of multivariate regression estimator can be improved by using Ranked set sampling. A bootstrap routine is developed in the statistical software R to perform inference when the sample size is small. We use a simulation study to investigate the performance of the method under known conditions and apply the method to the biomarker data collected in China Health and Nutrition Survey (CHNS 2009) data.

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Finite population corrections for ranked set sampling

Abstract: Linear range, observational economy, order statistics from finite populations, quadratic range, relative savings, sampling efficiency, sampling from finite populations, sampling without replacement,

Cited by 46 publications

References 3 publications

Design based estimation for ranked set sampling in finite populations

Design based estimation for ranked set sampling in finite populations

Best linear unbiased quantile estimators for environmental standards

On inference of multivariate means under ranked set sampling

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