Ranked Set Sampling Models and Methods

2016

In this study, we suggest different classes of Hartley-Ross type unbiased estimators for estimating the population mean (Ȳ ) of the study variable Y under ranked set sampling (RSS) and stratified ranked set sampling (StRSS) schemes, using known auxiliary information such as the population coefficient of variation (Cx), coefficient of kurtosis (β2x), coefficient of correlation (ρ), inter-quartile range (Qr), semi-quartile range (Qd) and semi-quartile average (Qa). Estimators are compared in terms of variances, percentage relative root mean squared error PRRMSE and percentage relative bias PRB. The variances of the proposed estimators are obtained up to first order of approximations. It is shown both theoretically and numerically, that proposed Hartley-Ross type unbiased estimators are more efficient than the usual mean estimator under RSS and StRSS schemes. Different ratio-type estimators using stratified double ranked set sampling (StDRSS) and stratified median ranked set sampling (...

This paper analyses the use of ranked set sampling procedures for obtaining the sub-sample from the set of nonrespondents. The first visit may serve for ranking accurately the sub-sampled non-respondents. The usual ranked set sample (rss) design and two variations of it : extreme-rss and median-rss are used for developing estimators of the population mean. Their expected variances and biases are obtained. A Monte Carlo experiment is developed for evaluating the behavior of the estimators. The use of rss appears as the best alternative.

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.

The problem of estimating the population mean is considered by McIntyre (1952). 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. RESUMEN El problema de estimar la media poblacional fue considerado por McIntyre (1952). Este sugirió un nuevo método de muestreo, llamado muestreo por conjuntos ordenados (Ranked Set Sampling, RSS) que consideraba como un método eficaz en comparación con el método del usual muestreo aleatorio simple. En los últimos años muchos autores sugirieron diversas modificaciones del RSS y les han usado en un amplio espectro de aplicaciones. En este trabajo se presenta una revisión de la literatura del método RSS así como algunas de sus modificaciones y aplicaciones.

2011

Stratified percentile ranked set sampling (SPRSS) method is suggested for estimating the population mean. The SPRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS) and stratified ranked set sampling (SRSS). It is shown that SPRSS estimator is an unbiased estimator of the population mean of symmetric distributions and is more efficient than its counterparts using SRS, SSRS and SRSS based on the same number of measured units.

Ranked set sampling is considered as a design for selecting a simple from a finite population. Generally it performs better than simple random sampling. Chen et al (2006) proposed a procedure for ranking categorical variables. This paper is concerned with the study of a sensitive variable. The randomized responses procedure due to Warner (1965) is used for eliminating answer biases. The variance of the proposed estimator is derived and it is larger than the proposal of Chen et al (2006). A study of the quality of the environment is developed. Direct responses and randomized responses estimators are compared. Ranking procedures used information provided by measurements of the contaminants in the air and the water.

Biometrical Journal, 2001

The problem of Ranked Set Sampling [RSS] is analyzed and a ratio estimator is proposed. A simple linear regression superpopulation model is proposed as a counterpart to the design approach. A predictor is developed by using shrinkage techniques.

Recent technological progress requires a fundamental review of the approach to quantitative log interpretation. A modern and advanced interpretation must be able to combine both quantitative and qualitative information from different sources, of different natures and at different scales. It should no longer focus only on solution of n equations of m unknowns with purely petrophysical goals. The recent introduction of imaging techniques has created a breakthrough in reservoir characterization. Because the reservoir can now be seen, it is possible to describe it in great detail as a three-dimensional organization of geological objects which are themselves classified as volumes, with their corresponding facies, bounded by surfaces with their own transmissivity properties. Petrophysical properties control the volume flow properties. The latter depend on the depositional facies attributes and the diagenetic effects undergone by the sediment since its deposition. They can be determined partly from standard logs, but more fully from borehole images that provide fundamental information about the reservoir anisotropy and the nature and distribution of reservoir heterogeneities. Surface attributes are defined through the shape, planarity, rugosity, extent, angular relationship, resistivity contrast, etc., of the surface. Practically all surfaces crossing a wellbore may be classified as they are detected by electrical imaging techniques from which their nature and origin can be precisely determined. Based on their origin and resistive characteristics transmissivity properties can be assigned to them. In addition, the influence of apparent dip can be taken into account in the response function of other tools. A modem and complete interpretation must, as far as possible, take into account all the accessible attributes at different scales, and from them determine the dynamic attributes associated with the reservoir. In addition, one can say that a succession of facies and surfaces defines a genetic sequence, itself limited by breaks of hierarchy and extent, and characterized by a set of attributes. A sequence and succession of sequences allow the recognition of the depositional environment that, consequently, has itself a set of attributes of higher rank, including seismic attributes. Finally, the reservoir geometry may be inferred from the determination of the depositional environment and the tectonic structure. The solution of this new truly global and integrated approach can be achieved through a generalization of the electrofacies concept. This is illustrated by examples.

Times of Israel (https://blogs.timesofisrael.com/the-old-hebrew-ishmael-papyrus-tapping-the-brakes/), 2022

On September 7, 2022, various press outlets ran stories about a First Temple Period Hebrew papyrus, with an Old Hebrew inscription, putatively dating to the late 7th/early 6th century BCE. Four lines of text are partially preserved, with the first extant word of the first extant line reading "To Ishmael." This article (by Prof. Christopher Rollston) was published in the Times of Israel, and includes a call for caution (i.e., tapping the brakes) with regard to some of the conclusions about this papyrus...especially since it was not found on an archaeological excavation, but rather was purchased (or received as a gift) in Israel and then ended up in Montana (thus, a very striking "chain of custody").