Random selection in ranked set sampling and its applications (original) (raw)
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Wiley Interdisciplinary Reviews: Computational Statistics, 2010
The most common sampling approach for collecting data from a population with the goal of making inferences about unknown features of the population is a simple random sample (SRS). There is a probabilistic guarantee that each measured observation in an SRS can be considered representative of the population. Despite this assurance, there remains a distinct possibility that a specific SRS might not provide a truly representative picture of the population. With that in mind, statisticians have developed a variety of ways to guard against obtaining such unrepresentative samples. Sampling designs such as stratified sampling, probability sampling, and cluster sampling all provide additional structure on the sampling process to improve the likelihood that the collected sample data do, indeed, provide a good representation of the population. A secondary goal in most data collection settings is to minimize the costs associated with obtaining the data. Ranked set sampling (RSS) is a relatively recent development that addresses both of these issues. It uses additional information from the population to provide more structure to the data collection process and decreases the likelihood of an unrepresentative sample. In addition, it is designed to minimize the number of measured observations required to achieve the desired precision in making inferences. In this article, we provide a general introduction to both balanced and unbalanced RSS, describing the basic approaches for collecting each type of RSS and some of the associated properties. We discuss a number of important factors that affect the performance of RSS procedures.
Some variations of ranked set sampling
2008
Balanced groups ranked set samples method (BGRSS) is suggested for estimating the population mean with samples of size k m 3 = where 1,2,...) = (k . The BGRSS sample mean is considered as an estimator of the population mean. It is found that the BGRSS produces unbiased estimators with smaller variance than the commonly used simple random sampling (SRS) for symmetric distributions considered in this study. For asymmetric distributions that we considered, the BGRSS estimators have a small bias. A real data set is used to illustrate the BGRSS method.
Environmental and Ecological Statistics, 2018
Rank-based sampling designs are powerful alternatives to simple random sampling (SRS) and often provide large improvements in the precision of estimators. In many environmental, ecological, agricultural, industrial and/or medical applications the interest lies in sampling designs that are cheaper than SRS and provide comparable estimates. In this paper, we propose a new variation of ranked set sampling (RSS) for estimating the population mean based on the random selection technique to measure a smaller number of observations than RSS design. We study the properties of the population mean estimator using the proposed design and provide conditions under which the mean estimator performs better than SRS and some existing rank-based sampling designs. Theoretical results are augmented with some numerical studies and a real-life example, where we also study the performance of our proposed design under perfect and imperfect ranking situations.
Improvement Over General And Wider Class of Estimators Using Ranked Set Sampling
International Journal of Scientific & Technology Research, 2012
Abstract: In this paper, Improvement over general and wider class of estimators of finite population means using ranked set sampling is investigated. Ranked set sampling (RSS) was first suggested to increase the efficiency of estimator of the population mean. The first order approximation to the bias and mean square error (MSE) of the investigated estimators are obtained. Theoretically, it is shown that these suggested estimators are more efficient than the general and wider class of estimators in simple random sampling.
REVIEW OF RANKED SET SAMPLING: MODIFICATIONS AND APPLICATIONS
The problem of estimating the population mean is considered by . A new sampling method is suggested, namely; ranked set sampling (RSS) as efficient method compared to the well known simple random sampling (SRS) method. In the last years many authors suggested different modifications of the RSS and used it in wide applications. In this paper, a literature review of the RSS method is presented as well as some its modifications and applications are provided.
Non-Parametric Selected Ranked Set Sampling
Biometrical Journal, 2001
A nonparametric selected ranked set sampling is suggested. The estimator of population mean based on the new approach is compared with that using the simple random sampling (SRS), the ranked set sampling (RSS) and the median ranked set sampling (MRSS) methods. The estimator of population mean using the new approach is found to be more efficient than its counterparts for almost all the cases considered.
Australian <html_ent glyph="@amp;" ascii="&"/> New Zealand Journal of Statistics, 2001
This paper proposes a sampling procedure called selected ranked set sampling (SRSS), in which only selected observations from a ranked set sample (RSS) are measured. This paper describes the optimal linear estimation of location and scale parameters based on SRSS, and for some distributions it presents the required tables for optimal selections. For these distributions, the optimal SRSS estimators are compared with the other popular simple random sample (SRS) and RSS estimators. In every situation the estimators based on SRSS are found advantageous at least in some respect, compared to those obtained from SRS or RSS. The SRSS method with errors in ranking is also described. The relative precision of the estimator of the population mean is investigated for different degrees of correlations between the actual and erroneous ranking. The paper reports the minimum value of the correlation coefficient between the actual and the erroneous ranking required for achieving better precision with respect to the usual SRS estimator and with respect to the RSS estimator.
An Efficient Class of Estimators for the Finite Population Mean in Ranked Set Sampling
Open Journal of Statistics, 2016
In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.
Ranked set sampling: its essence and some new applications
Environmental and Ecological Statistics, 2007
Ranked set sampling is a simple idea of great use. It was proposed half a century ago. The last 15 years or so have witnessed considerable development in the research and applications of ranked set sampling. In this paper, we give an overview on ranked set sampling. We review several variants of ranked set sampling developed since the original idea was proposed. We discuss the essence and the theoretical foundation of ranked set sampling. We present some novel applications of ranked set sampling in areas such as clinical trials, genetic quantitative trait loci mappings and others. By doing so, we wish to provide the reader with a philosophical view on ranked set sampling and shed some lights on a broader range of its applications.
www.ijstr.org Improvement Over General And Wider Class of Estimators Using Ranked Set Sampling
2015
Abstract: In this paper, Improvement over general and wider class of estimators of finite population means using ranked set sampling is investigated. Ranked set sampling (RSS) was first suggested to increase the efficiency of estimator of the population mean. The first order approximation to the bias and mean square error (MSE) of the investigated estimators are obtained. Theoretically, it is shown that these suggested estimators are more efficient than the general and wider class of estimators in simple random sampling.