General ranked set sampling for efficient treatment comparisons

In treatment comparison experiments, the treatment responses are often correlated with some concomitant variables which can be measured before or at the beginning of the experiments. In this article, we propose schemes for the assignment of experimental units that may greatly improve the efficiency of the comparison in such situations. The proposed schemes are based on general ranked set sampling. The relative efficiency and cost-effectiveness of the proposed schemes are studied and compared. It is found that some proposed schemes are always more efficient than the traditional simple random assignment scheme when the total cost is the same. Numerical studies show promising results using the proposed schemes.

General ranked set sampling with cost considerations

Nahhas, Wolfe, and Chen (2002, Biometrics 58, 964-971) considered optimal set size for ranked set sampling (RSS) with fixed operational costs. This framework can be very useful in practice to determine whether RSS is beneficial and to obtain the optimal set size that minimizes the variance of the population estimator for a fixed total cost. In this article, we propose a scheme of general RSS in which more than one observation can be taken from each ranked set. This is shown to be more cost-effective in some cases when the cost of ranking is not so small. We demonstrate using the example in Nahhas, Wolfe, and Chen (2002, Biometrics 58, 964-971), by taking two or more observations from one set even with the optimal set size from the RSS design can be more beneficial.

Efficient regression analysis with ranked-set sampling

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.

Selected Ranked Set Sampling

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.

The efficiency of improved ranked set sampling methods

Ranked set sampling is a desirable sampling technique where the ranking of the sample observations does not require the actual measurement. This thesis develops new ranked set sampling techniques and determines the sampling characteristics required to best estimate the required population parameters, such as mean and variance.

A connection between two nonparametric tests for perfect ranking in balanced ranked set sampling

In this note, we show that an extension of a test for perfect ranking in a balanced ranked set sample given by Li and Balakrishnan (2008) to the multi-cycle case turns out to be equivalent to the test statistic proposed by Frey et al. (2007). This provides an alternative interpretation and motivation for their test statistic.

A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors.

Variance estimation in ranked set sampling using a concomitant variable

We propose a nonparametric variance estimator when ranked set sampling (RSS) and judgment post stratification (JPS) are applied by measuring a concomitant variable. Our proposed estimator is obtained by conditioning on observed concomitant values and using nonparametric kernel regression.

Optimal sign tests for data from ranked set samples

This paper considers the one-sample sign test for data obtained from general ranked set sampling when the number of observations for each rank are not necessarily the same, and proposes a weighted sign test because observations with different ranks are not identically distributed. The optimal weight for each observation is distribution free and only depends on its associated rank. It is shown analytically that (1) the weighted version always improves the Pitman efficiency for all distributions; and (2) the optimal design is to select the median from each ranked set.

Efficient designs for sampling and subsampling in fisheries research based on ranked sets

Sampling strategies are developed based on the idea of ranked set sampling (RSS) to increase efficiency and therefore to reduce the cost of sampling in fishery research. The RSS incorporates information on concomitant variables that are correlated with the variable of interest in the selection of samples. For example, estimating a monitoring survey abundance index would be more efficient if the sampling sites were selected based on the information from previous surveys or catch rates of the fishery. We use two practical fishery examples to demonstrate the approach: site selection for a fishery-independent monitoring survey in the Australian northern prawn fishery (NPF) and fish age prediction by simple linear regression modelling a short-lived tropical clupeoid. The relative efficiencies of the new designs were derived analytically and compared with the traditional simple random sampling (SRS). Optimal sampling schemes were measured by different optimality criteria. For the NPF monitoring survey, the efficiency in terms of variance or mean squared errors of the estimated mean abundance index ranged from 114 to 199% compared with the SRS. In the case of a fish ageing study for Tenualosa ilisha in Bangladesh, the efficiency of age prediction from fish body weight reached 140%.

Temporal trends (2000–2011) and influences on fishery-independent catch rates for loggerhead sea turtles (Caretta caretta) at an important coastal foraging region in the southeastern United States

Seasonal trawling was conducted randomly in coastal (depths of 4.6–17 m) waters from St. Augustine, Florida, (29.9°N) to Winyah Bay, South Carolina (33.1°N), during 2000–03, 2008–09, and 2011 to assess annual trends in the relative abundance of sea turtles. A total of 1262 loggerhead sea turtles (Caretta caretta) were captured in 23% (951) of 4207 sampling events. Capture rates (overall and among prevalent 5-cm size classes) were analyzed through the use of a generalized linear model with log link function for the 4097 events that had complete observations for all 25 model parameters. Final models explained 6.6% (70.1–75.0 cm minimum straight-line carapace length [SCLmin]) to 14.9% (75.1–80.0 cm SCLmin) of deviance in the data set. Sampling year, geographic subregion, and distance from shore were retained as significant terms in all final models, and these terms collectively accounted for 6.2% of overall model deviance (range: 4.5–11.7% of variance among 5-cm size classes). We retained 18 parameters only in a subset of final models: 4 as exclusively significant terms, 5 as a mixture of significant or nonsignificant terms, and 9 as exclusively nonsignificant terms. Four parameters also were dropped completely from all final models. The generalized linear model proved appropriate for monitoring trends for this data set that was laden with zero values for catches and was compiled for a globally protected species. Because we could not account for much model deviance, metrics other than those examined in our study may better explain catch variability and, once elucidated, their inclusion in the generalized linear model should improve model fits.

Statistical Inference for Computable General Equilibrium Models with Application to a Model of the Moroccan Economy

We study the problem of measuring the uncertainty of CGE (or RBC)-type model simulations associated with parameter uncertainty. We describe two approaches for building confidence sets on model endogenous variables. The first one uses a standard Wald-type statistic. The second approach assumes that a confidence set (sampling or Bayesian) is available for the free parameters, from which confidence sets are derived by a projection technique. The latter has two advantages: first, confidence set validity is not affected by model nonlinearities; second, we can easily build simultaneous confidence intervals for an unlimited number of variables. We study conditions under which these confidence sets take the form of intervals and show they can be implemented using standard methods for solving CGE models. We present an application to a CGE model of the Moroccan economy to study the effects of policy-induced increases of transfers from Moroccan expatriates.

Research priorities for child and adolescent physical activity and sedentary behaviours: an international perspective using a twin-panel Delphi procedure

Background
The quantity and quality of studies in child and adolescent physical activity and sedentary behaviour have rapidly increased, but research directions are often pursued in a reactive and uncoordinated manner.

Aim
To arrive at an international consensus on research priorities in the area of child and adolescent physical activity and sedentary behaviour.

Methods
Two independent panels, each consisting of 12 experts, undertook three rounds of a Delphi methodology. The Delphi methodology required experts to anonymously answer questions put forward by the researchers with feedback provided between each round.

Results
The primary outcome of the study was a ranked set of 29 research priorities that aimed to be applicable for the next 10 years. The top three ranked priorities were: developing effective and sustainable interventions to increase children’s physical activity long-term; policy and/or environmental change and their influence on children’s physical activity and sedentary behaviour; and prospective, longitudinal studies of the independent effects of physical activity and sedentary behaviour on health.

Conclusions
These research priorities can help to guide decisions on future research directions.