The Relative Efficiency of Ranked Set Sampling in Ordinary Least Squares Regression

Ranked set sampling was developed for situations where measurement cost is expensive compared with unit acquisition. This paper presents results of simulations and theory examining the impact of balanced ranked set sampling on the relative efficiencies of the slope and intercept estimators of an ordinary least squares regression. Perfect ranking of either the independent or the dependent variable is assumed throughout. In contradistinction to most of the published ranked set sampling work, it is demonstrated that balanced ranked set sampling offers at most little improvement in the relative efficiencies of the slope estimator at any sample size.     

Bayes Estimation of a Distribution Function Using Ranked Set Samples

Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics gener- ated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environ- mental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based on the EM Algorithm is used to produce the GMLE of F. For the case of squared error loss, simple solutions are uncommon, and a procedure to find the solution to the Bayes estimate using the Gibbs sampler is illustrated. The methods are illustrated with data from the Natural Environmental Research Council of Great Britain (1975), representing water discharge of floods on the Nidd River in Yorkshire, England     

Estimation of Normal Variance Based on Balanced and Unbalanced Ranked Set Samples

In this paper we address the problem of estimation of the variance of a normal population based on a balanced as well as an unbalanced ranked set sample (RSS), which is a modification of the original RSS of McIntyre (1952).We have proposed several methods of estimation of variance by combining different unbiased between and within estimators, and compared their performances     

Ranked set sampling: an annotated bibliography

The paper provides an up-to-date annotated bibliography of the literature on ranked set sampling. The bibliography includes all pertinent papers known to the authors, and is intended to cover applications as well as theoretical developments. The annotations are arranged in chronological order and are intended to be sufficiently complete and detailed that a reading from beginning to end would provide a statistically mature reader with a state-of-the-art survey of ranked set sampling, including historical development, current status, and future research directions and applications. A final section of the paper gives a listing of all annotated papers, arranged in alphabetical order by author.This paper was prepared with partial support from the United States Environmental Protection Agency under a Cooperative Agreement Number CR-821531. The contents have not been subject to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.     

Ranked set sampling: its essence and some new applications

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.     

Ranked set sample design for environmental investigations

Ranked set sampling can provide an efficient basis for estimating parameters of environmental variables, particularly when sampling costs are intrinsically high. Various ranked set estimators are considered for the population mean and contrasted in terms of their efficiencies and useful- ness, with special concern for sample design considerations. Specifically, we consider the effects of the form of the underlying random variable, optimisation of efficiency and how to allocate sampling effort for best effect (e.g. one large sample or several smaller ones of the same total size). The various prospects are explored for two important positively skew random variables (lognormal and extreme value) and explicit results are given for these cases. Whilst it turns out that the best approach is to use the largest possible single sample and the optimal ranked set best linear estimator (ranked set BLUE), we find some interesting qualitatively different conclusions for the two skew distributions     

Sampling variability and estimates of density dependence: a composite-likelihood approach

It is well known that sampling variability, if not properly taken into account, affects various ecologically important analyses. Statistical inference for stochastic population dynamics models is difficult when, in addition to the process error, there is also sampling error. The standard maximum-likelihood approach suffers from large computational burden. In this paper, I discuss an application of the composite-likelihood method for estimation of the parameters of the Gompertz model in the presence of sampling variability. The main advantage of the method of composite likelihood is that it reduces the computational burden substantially with little loss of statistical efficiency. Missing observations are a common problem with many ecological time series. The method of composite likelihood can accommodate missing observations in a straightforward fashion. Environmental conditions also affect the parameters of stochastic population dynamics models. This method is shown to handle such nonstationary population dynamics processes as well. Many ecological time series are short, and statistical inferences based on such short time series tend to be less precise. However, spatial replications of short time series provide an opportunity to increase the effective sample size. Application of likelihood-based methods for spatial time-series data for population dynamics models is computationally prohibitive. The method of composite likelihood is shown to have significantly less computational burden, making it possible to analyze large spatial time-series data. After discussing the methodology in general terms, I illustrate its use by analyzing a time series of counts of American Redstart (Setophaga ruticilla) from the Breeding Bird Survey data, San Joaquin kit fox (Vulpes macrotis mutica) population abundance data, and spatial time series of Bull trout (Salvelinus confluentus) redds count data.     

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.     

Science or Slaughter: Need for Lethal Sampling of Sharks

Abstract: General consensus among scientists, commercial interests, and the public regarding the status of shark populations is leading to an increasing need for the scientific community to provide information to help guide effective management and conservation actions. Experience from other marine vertebrate taxa suggests that public, political, and media pressures will play an increasingly important part in setting research, management, and conservation priorities. We examined the potential implications of nonscientific influences on shark research. In particular, we considered whether lethal research sampling of sharks is justified. Although lethal sampling comes at a cost to a population, especially for threatened species, the conservation benefits from well‐designed studies provide essential data that cannot be collected currently in any other way. Methods that enable nonlethal collection of life‐history data on sharks are being developed (e.g., use of blood samples to detect maturity), but in the near future they will not provide widespread or significant benefits. Development of these techniques needs to continue, as does the way in which scientists coordinate their use of material collected during lethal sampling. For almost half of the known shark species there are insufficient data to determine their population status; thus, there is an ongoing need for further collection of scientific data to ensure all shark populations have a future. Shark populations will benefit most when decisions about the use of lethal sampling are made on the basis of scientific evidence that is free from individual, political, public, and media pressures.     

新型甲醛被动式检气管的研制

新研制的甲醛被动式检气管是建立在气体分子扩散和化学吸收原理基础上的，检气管内的惰性担体上浸渍了对甲醛特效的希夫试剂。当管内进入甲醛气体时，即发生显色反应，检气管的显色长度的平方与甲醛浓度及采样时间的乘积成线性关系。检出下限为０．０１５ｍｇ＃Ｌ（采样５ｈ），它集采样与分析为一体，结构简单，不需动力，便于携带和操作方便，应用于检测某厂刨花板车间和制胶车间的甲醛气体，与传统的注射器采样比色分析法对比，结     

Developing a Sampling Strategy for Baptisia arachnifera Based on Allozyme Diversity

We analyzed the amount and distribution of genetic variation in Baptisia arachnifera Duncan to develop a sampling strategy for ex situ research. Baptisia arachnifera is an endangered plant species endemic to the coastal plain of Georgia (U.S.) where all populations are within 16 km of each other. A reduction in numbers of individuals has been observed during the last 50 years. Baptisia arachnifera was polymorphic at 24% of the 37 loci examined with an average of 1.32 alleles per locus. The genetic diversity index was relatively low ( H_e = 0.097) as expected for endemic species. Populations were in Hardy-Weinberg equilibrium, suggesting that the species is outcrossing. Consistent with this conclusion is the observation that the majority (approximately 90%) of the genetic variation present in the species is found within individual populations. Indirect evidence of gene flow between populations was detected (   Nm = 2.35). The close proximity of the populations and the recent reduction in population sizes suggest that the populations surveyed may be fragments of a once more continuous gene pool. Based on the observed distribution of genetic diversity among populations (G_ST = 0.096), sampling two populations would capture 99% of the allozyme diversity surveyed. Allozyme data were used to determine which 2 of the 10 populations surveyed should be sampled to maximize the ex situ conservation of genetic diversity. Although the paper-producing companies that own most of the land where Baptisia arachnifera occurs are modifying their harvesting techniques, the species could become extinct without more effective management and preservation efforts.     

Nonparametric Ranked-set Sampling Confidence Intervals for Quantiles of a Finite Population

Ranked-set sampling from a finite population is considered in this paper. Three sampling protocols are described, and procedures for constructing nonparametric confidence intervals for a population quantile are developed. Algorithms for computing coverage probabilities for these confidence intervals are presented, and the use of interpolated confidence intervals is recommended as a means to approximately achieve coverage probabilities that cannot be achieved exactly. A simulation study based on finite populations of sizes 20, 30, 40, and 50 shows that the three sampling protocols follow a strict ordering in terms of the average lengths of the confidence intervals they produce. This study also shows that all three ranked-set sampling protocols tend to produce confidence intervals shorter than those produced by simple random sampling, with the difference being substantial for two of the protocols. The interpolated confidence intervals are shown to achieve coverage probabilities quite close to their nominal levels. Rankings done according to a highly correlated concomitant variable are shown to reduce the level of the confidence intervals only minimally. An example to illustrate the construction of confidence intervals according to this methodology is provided.     

Sampling from partially rank-ordered sets

In this paper we introduce a new sampling design. The proposed design is similar to a ranked set sampling (RSS) design with a clear difference that rankers are allowed to declare any two or more units are tied in ranks whenever the units can not be ranked with high confidence. These units are replaced in judgment subsets. The fully measured units are then selected from these partially ordered judgment subsets. Based on this sampling scheme, we develop unbiased estimators for the population mean and variance. We show that the proposed sampling procedure has some advantages over standard ranked set sampling.     

Detecting Rare Species with Random or Subjective Sampling: a Case Study of Red-Listed Saproxylic Beetles in Boreal Sweden

Abstract:  Efficient sampling design in field studies is important for economical and statistical reasons. We compared two ways to distribute sampling effort over an area, either randomly or subjectively. We searched for red-listed saproxylic (wood-living) beetles in 30 spruce stands in boreal Sweden by sifting wood from dead trees. We randomly selected positions within each stand with a geographic positioning system and sampled the nearest dead tree (random sample). In the same stand we also sampled dead trees that, based on literature, were likely to host such species (subjective sampling). The subjective sampling (two to five samples per stand, depending on stand size) was compared with the higher, random sampling effort (fixed level of 12 samples/stand). Subjective sampling was significantly more efficient. Red-listed species were found in 36% of the subjective samples and in 16% of the random samples. Nevertheless, the larger random effort resulted in a comparable number of red-listed species per stand and in 13 detected species in total (vs. 12 species with subjective sampling). Random sampling was less efficient, but provided an unbiased alternative more suitable for statistical purposes, as needed in, for example, monitoring programs. Moreover, new species-specific knowledge can be gained through random searches.     

Factors Leading to Different Viability Predictions for a Grizzly Bear Data Set

Population viability analysis programs are being used increasingly in research and management applications, but there has not been a systematic study of the congruence of different program predictions based on a single data set. We performed such an analysis using four population viability analysis computer programs: GAPPS, INMAT, RAMAS/AGE, and VORTEX. The standardized demographic rates used in all programs were generalized from hypothetical increasing and decreasing grizzly bear ( Ursus arctos horribilis ) populations. Idiosyncracies of input format for each program led to minor differences in intrinsic growth rates that translated into striking differences in estimates of extinction rates and expected population size. In contrast, the addition of demographic stochasticity, environmental stochasticity, and inbreeding costs caused only a small divergence in viability predictions. But, the addition of density dependence caused large deviations between the programs despite our best attempts to use the same density-dependent functions. Population viability programs differ in how density dependence is incorporated, and the necessary functions are difficult to parameterize accurately. Thus, we recommend that unless data clearly suggest a particular density-dependent model, predictions based on population viability analysis should include at least one scenario without density dependence. Further, we describe output metrics that may differ between programs; development of future software could benefit from standardized input and output formats across different programs.     

Sampling biological characteristics of krill: Effect of heterogeneous nature of swarms

An effect of the very patchy distribution of Antarctic krill (Euphausia superba Dana) in various forms of aggregation is that a single swarm may not provide an unbiased estimate of population parameters such as mean length of krill in the local area. Here, we analyse the number of samples required to estimate the characteristics of a local population as precisely as if there were no differences between krill swarms in terms of their biological composition. Krill were intensively sampled over different spatial and temporal scales around South Georgia in 1981 and 1982, and in the Bransfield Strait in 1985. These varied from replicate hauls at a single station over 24 h and repeat sampling in restricted areas over periods of 6 to 14 d to regional surveys around South Georgia and in the Bransfield Strait. Various biological characteristics were measured such as length, maturity, moult stage and feeding state. Depending upon the biological characteristic examined and the area covered by the sampling programme, the number of samples needed to obtain the same degree of precision as would be found in the absence of heterogeneity varied from 3 to > 80 samples. This has important implications for the design of net-sampling programme for monitoring krill populations.