Optimal ranked set sampling estimation based on medians from multiple set sizes

Gemayel, Nader; Stasny, Elizabeth A.; Wolfe, Douglas A.

doi:10.1080/10485250903301517

Cited by 10 publications

(3 citation statements)

References 11 publications

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“…. , m, from the population for the purpose of ranking and finally nominating m sampling units (one from each set) for sizes in random helps to apply the RNS scheme in circumstances where the set size might be random (see Boyles and Samaniego (1986) and Gemayel et al (2010)). Another advantage of allowing the set size to be random is that, when ρ 1 > 0, randomized nomination sample is expected to contain a simple random sample of size mρ 1 in addition to a collection of extremal order statistics from various set sizes, which contain more information about the underlying population than SRS.…”

Section: Introductionmentioning

confidence: 99%

Parametric inference for proportional (reverse) hazard rate models with nomination sampling

Nourmohammadi¹,

Jozani²,

Johnson³

2015

Preprint

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Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental and ecological applications.In this paper, we investigate parametric inference using RNS design for estimating the unknown vector of parameters θ θ θ in the proportional hazard rate and proportional reverse hazard rate models.We examine both maximum likelihood (ML) and method of moments (MM) methods and investigate the relative precision of our proposed RNS-based estimators compared with those based on simple random sampling (SRS). We introduce four types of RNS-based data as well as necessary EM algorithms for the ML estimation, and evaluate the performance of corresponding estimators in estimating θ θ θ. We show that there are always values of the design parameters on which RNS-based estimators are more efficient than those based on SRS. Inference based on imperfect ranking is also explored and it is shown that the improvement holds even when the ranking is imperfect. Theoretical results are augmented with numerical evaluations and a case study.

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Section: Introductionmentioning

confidence: 99%

Parametric inference for proportional (reverse) hazard rate models with nomination sampling

Nourmohammadi¹,

Jozani²,

Johnson³

2015

Preprint

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“…One alternative in such situations is to pare down the larger sets to agree in size with the smaller sets, but that can lead to a loss of valuable information that could have been obtained from the more comprehensive rankings within the larger sets. Gemayel et al 75 propose an estimator for the median of a symmetric population that combines medians of ranked set samples of varying sizes. While not optimal for any specific symmetric distribution, they show that the estimator is robust over a wide class of symmetric distributions.…”

Section: Unequal Set Sizesmentioning

confidence: 99%

Integrating approach to size and site at a sanitary landfill in Selangor state, Malaysia

Younes

Basri

Nopiaha

et al. 2015

Environmental Engineering Research

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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.

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“…Such a design is unbalanced to the extreme. Beyond that, RSS procedures can be envisaged that involve multiple set sizes in a single application (Gemayel et al 2010).…”

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confidence: 99%

Bayesian nonparametric models for ranked set sampling

2014

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Ranked set sampling (RSS) is a data collection technique that combines measurement with judgment ranking for statistical inference. This paper lays out a formal and natural Bayesian framework for RSS that is analogous to its frequentist justification, and that does not require the assumption of perfect ranking or use of any imperfect ranking models. Prior beliefs about the judgment order statistic distributions and their interdependence are embodied by a nonparametric prior distribution. Posterior inference is carried out by means of Markov chain Monte Carlo techniques, and yields estimators of the judgment order statistic distributions (and of functionals of those distributions).

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Optimal ranked set sampling estimation based on medians from multiple set sizes

Cited by 10 publications

References 11 publications

Parametric inference for proportional (reverse) hazard rate models with nomination sampling

Parametric inference for proportional (reverse) hazard rate models with nomination sampling

Integrating approach to size and site at a sanitary landfill in Selangor state, Malaysia

Bayesian nonparametric models for ranked set sampling

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