Nomination Sampling Research Articles

Statistical inference from partially nominated sets: An application to estimating the prevalence of osteoporosis among adult women

This paper focuses on drawing statistical inference based on a novel variant of maxima or minima nomination sampling (NS) designs. These sampling designs are useful for obtaining more representative sample units from the tails of the population distribution using the available auxiliary ranking information. However, one common difficulty in performing NS in practice is that the researcher cannot obtain a nominated sample unless he/she uniquely determines the sample unit with the highest or the lowest rank in each set. To overcome this problem, a variant of NS, which is called partial nomination sampling, is proposed, in which the researcher is allowed to declare that two or more units are tied in the ranks whenever he/she cannot find the sample unit with the highest or the lowest rank. Based on this sampling design, two asymptotically unbiased estimators are developed for the cumulative distribution function, which is obtained using maximum likelihood and moment-based approaches, and their asymptotic normalities are proved. Several numerical studies have shown that the proposed estimators have higher relative efficiencies than their counterparts in simple random sampling in analyzing either the upper or the lower tail of the parent distribution. The procedures that we developed are then implemented on a real dataset from the Third National Health and Nutrition Examination Survey (NHANES III) to estimate the prevalence of osteoporosis among adult women aged 50 and over. It is shown that in certain circumstances, the techniques that we have developed require only one-third of the sample size needed in SRS to achieve the desired precision. This results in a considerable reduction in time and cost compared to the standard SRS method.

Using nomination sampling in estimating the area under the ROC curve

Using nomination sampling in estimating the area under the ROC curve

Expect the Unexpected: A Qualitative Study of the Ripple Effects of Children's Mental Health Services Implementation Efforts.

Strategies to implement evidence-based interventions (EBIs) in children's mental health services have complex direct and indirect causal impacts on multiple outcomes. Ripple effects are outcomes caused by EBI implementation efforts that are unplanned, unanticipated, and/or more salient to stakeholders other than researchers and implementers. The purpose of the current paper is to provide a compilation of possible ripple effects associated with EBI implementation strategies in children's mental health services, to be used for implementation planning, research, and quality improvement. Participants were identified via expert nomination and snowball sampling. Online surveys were completed by 81 participants, each representing one of five roles: providers of mental health services to children or youth, researchers, policy makers, caregivers, and youth. A partially directed conventional content analysis with consensus decision making was used to code ripple effects. Four hundred and four unique responses were coded into 66 ripple effects and 14 categories. Categories include general knowledge, skills, attitudes, and confidence about using EBIs; general job-related ripple effects; EBI treatment adherence, fidelity, and alignment; gaming the system; equity and stigma; shifting roles, role clarity, and task shifting; economic costs and benefits; EBI treatment availability, access, participation, attendance, barriers, and facilitators; clinical process and treatment quality; client engagement, therapeutic alliance, and client satisfaction; clinical organization structure, relationships in the organization, process, and functioning; youth client and caregiver outcomes; and use of EBI strategies and insights in one's own life. This research advances the field by providing children's mental health implementers, researchers, funders, policy makers, and consumers with a menu of potential ripple effects. It can be a practical tool to ensure compliance with guidance from Quality Improvement/Quality Assurance, Complexity Science, and Diffusion of Innovation Theory. Future phases will match potential ripple effects with salient children's mental health implementation strategies for each participant role.

An improved exponentially weighted moving average chart for monitoring proportions using maxima nomination sampling

We develop a new proportion control chart using the exponentially weighted moving average (EWMA) for the maxima nomination sampling (MNS) method. By using average run length (ARL), we compare it with conventional Shewhart and EWMA control charts based on the simple random sampling (SRS) method. We study the effect of the sample size, the set size, the in-control and out-of-control non-conforming proportion, the smoothing parameter, and the refinement factor on the performance of MNS-EWMA charts using ARL curves. We show that the MNS-EWMA control chart is an excellent indicator of changes in the quality of processes relative to SRS-Shewhart and SRS-EWMA charts. We present optimal ranges for the smoothing parameter of MNS-EWMA charts. An illustrative example with simulated data is enclosed. The results show that MNS-EWMA control charts produce significant enhancement over the traditional charts based on SRS.

An economic design of rectifying single sampling plans via maxima nomination sampling in the presence of inspection errors

Economic design for acceptance sampling plans (ASP) has attracted the attention of many researchers. In this article, rectifying single ASP is checked by using the maxima nomination sampling method and the plan’s parameters are obtained while sum of consumer and producer loss is minimized. In the presence of inspection errors, the lots are rectified in two ways: the detected defective items are discarded or replaced with non-defective items. To illustrate the advantages of the economic design of MNS, it is compared with SRS plan by using a real world example.

Parametric Inference Using Nomination Sampling with an Application to Mercury Contamination in Fish

Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental, agricultural, medical and ecological applications. In this paper, we investigate parametric inference using RNS design for estimating an unknown vector of parameters θ in some parametric families of distributions. We examine both maximum likelihood (ML) and method of moments (MM) approaches. We introduce four types of RNS-based data as well as necessary EM algorithms for the ML estimation under each data type, and evaluate the performance of corresponding estimators in estimating θ compared with those based on simple random sampling (SRS). Our results can address many parametric inference problems in reliability theory, sport analytics, fisheries, etc. Theoretical results are augmented with numerical evaluations, where we also study inference based on imperfect ranking. We apply our methods to a real data problem in order to study the distribution of the mercury contamination in fish body using RNS designs.

Designing an economical acceptance sampling plan in the presence of inspection errors based on maxima nomination sampling method

One of the most useful and effective methods with an extensive application in companies with purpose of examining the quality of the raw material in addition to final products, is acceptance sampling plans. The inspection process is assumed free of errors in most design of acceptance sampling plans. However, this assumption may not be true. In this research, an optimization model for acceptance sampling plan based on the Maxima Nomination Sampling (MNS) method which is developed for single acceptance sampling plan at the presence of inspection errors is presented. What we have accomplished in this article is to propose an economical model which involves two types of inspection errors and investigates the impact of these errors from an economical point of view then it's been compared with the a classical method for proving it 's efficiency. Furthermore, the sensitivity analysis is carried out to analyze the behavior of the MNS scheme optimal solution. The numerical studies indicate that MNS method is always more economical than classical one.

Quantile regression with nominated samples: An application to a bone mineral density study.

This paper studies quantile regression analysis with maxima or minima nomination sampling designs. These designs are often used to obtain more representative samples from the tails of the underlying distribution using the easy to access rank information during the sampling process. We propose new loss functions to incorporate the rank information of nominated samples in the estimation process. Also, we provide an alternative approach that translates estimation problems with nominated samples to corresponding problems under simple random sampling (SRS). Strategies are given to choose proper nomination sampling designs for a given population quantile. Numerical studies show that quantile regression models with maxima (or minima) nominated samples have higher relative efficiencies compared with their counterparts under SRS for analyzing the upper (or lower) tail quantiles of the distribution of the response variable. Results are then implemented on a large cohort study in the Canadian province of Manitoba to analyze quantiles of bone mineral density using available covariates. We show that in some cases, methods based on nomination sampling designs require about one-tenth of the sample used in SRS to estimate the lower or upper tail conditional quantiles with comparable mean squared errors. This is a dramatic reduction in time and cost compared with the usual SRS approach.

An Economic Design of Rectifying Double Acceptance Sampling Plans via Maxima Nomination Sampling

AbstractIn industry when a lot of items is sent for inspection, double acceptance sampling plans (DASP) are considered as a way to decide on acceptance or rejection of the lot. If the lot contains items with high sensitivity, then the measuring of quality characteristics is destructive or costly. So we are looking for a method to decide that it has high performance. Using the ranked set sampling (RSS) method will make it stricter and more accurate whether or not to accept a lot. Moreover, it is affordable and will not burden extra costs on the buyer or the producer. In this paper, by using a special type of RSS, with the name of maxima nomination sampling (MNS), we design a DASP with regards to the total loss function. The results indicate that the total loss function, which is acquired by the MNS method, has lower values than the one using the simple random sampling (SRS) method.

A new economical scheme of acceptance sampling plan in a two-stage approach based on the maxima nomination sampling technique

An acceptance sampling plan plays a very important role in any quality assurance system. In this new economical design of acceptance sampling plan, three types of costs are included in the objective function by considering average outgoing quality limit (AOQL), average quality level (AQL) and lot tolerance percent defective (LTPD) constraints based on the maxima nomination sampling (MNS) method in a two-stage approach. The design of this sampling inspection plan involves the minimum average total inspection (ATI). The model is designed to minimize the summation of costs and the proposed MNS economical sampling plan is compared with the classical one. Practitioners can use the proposed model to decrease the total cost of inspection.

Distribution-free tolerance intervals with nomination samples: Applications to mercury contamination in fish

Tolerance intervals are enclosure intervals which will cover a fixed portion of the population distribution with a specified confidence. These intervals are widely used in clinical, environmental, biological and industrial applications, including quality control and environmental monitoring, to help determine limits for detection or assessment monitoring. In many of these applications the measurement of the variable of interest is costly and/or destructive but a small number of sampling units can be ranked easily by using expert-opinion knowledge or inexpensive and easily obtained measurements from these units. In this paper, we construct tolerance intervals based on the expensive measurements that are obtained using randomized nomination sampling (RNS) with the help of inexpensive auxiliary information. We study the performance of our proposed RNS-based tolerance intervals based on the corresponding coverage probabilities and the necessary sample size for their existence with those based on simple random sampling (SRS). The efficiency of the constructed RNS-based tolerance intervals compared to their SRS counterparts is discussed. We investigate the performance of RNS-based tolerance intervals for different values of the design parameters and various population shapes. We find the values of the design parameters which improve RNS over SRS. The RNS design in presence of ranking error is discussed and a new method for estimating ranking error probabilities is proposed. Theoretical results are augmented with numerical evaluations and a case study based on a fish mercury level dataset.

Nonparametric Confidence Intervals for Quantiles with Randomized Nomination Sampling

Rank-based sampling methods have a wide range of applications in environmental and ecological studies as well as medical research and they have been shown to perform better than simple random sampling (SRS) for estimating several parameters in finite populations. In this paper, we obtain nonparametric confidence intervals for quantiles based on randomized nomination sampling (RNS) from continuous distributions. The proposed RNS confidence intervals provide higher coverage probabilities and their expected length, especially for lower and upper quantiles, can be substantially shorter than their counterparts under SRS design. We observe that a design parameter associated with the RNS design allows one to construct confidence intervals with the exact desired coverage probabilities for a wide range of population quantiles without the use of randomized procedures. Theoretical results are augmented with numerical evaluations and a case study based on a livestock data set. Recommendations for choosing the RNS design parameters are made to achieve shorter RNS confidence intervals than SRS design and these perform well even when ranking is imperfect.

Confidence intervals for quantiles in finite populations with randomized nomination sampling

Given a finite population consisting of N elements, it is desired to obtain confidence intervals for (t/N)th quantile x(t) of the population based on the randomized nomination sampling (RNS) design. Three without replacement sampling protocols are described and procedures for constructing nonparametric confidence intervals for population quantiles are developed. Formulas for computing coverage probabilities for these confidence intervals are presented. Simulation studies are conducted and the performance of the RNS based confidence intervals is compared with those based on the simple random sample without replacement design.

HIV Disease Burden and Related Risk Behaviours Among Men Who Have Sex with Men in Yuxi Prefecture, Yunnan Province, China: 2010−2011

The HIV epidemic is rapidly increasing among men who have sex with men (MSM) in China. Data on the disease burden and risk behaviours of MSM related to HIV transmission are needed to inform education and prevention programs. We conducted two cross-sectional surveys among MSM in Yuxi Prefecture in Yunnan Province, China, during 2010-2011. Men were recruited by snowball (participant referrals) and nomination sampling methods at gay-oriented venues and hotspots. Participants were asked to complete a 20-min anonymous questionnaire. Blood samples were collected to determine HIV status and the BED capture enzyme immunoassay was used to estimate the incidence rate. A total of 288 MSM participated in this study across the two surveys. The two-year overall HIV prevalence was 10.7% and the estimated incidence rate was 5.4 per 100 person-years (95% CI 1.1-9.6). A reported 37.2% of MSM were married to a female and 35.1% had sex with a female in the past 6months. Condom use with male partners (81.4-93.0%) and female partners (56.3-77.4%) at the last penetrative act significantly increased between the survey conducted in 2010 and the survey in 2011. HIV prevalence is high among Chinese MSM in Yunnan. Common bisexual behaviours and low consistent condom use with female partners suggest a potential spread of HIV from MSM to females.

Randomized nomination sampling for finite populations

We propose a randomized minima–maxima nomination (RMMN) sampling design for use in finite populations. We derive the first- and second-order inclusion probabilities for both with and without replacement variations of the design. The inclusion probabilities for the without replacement variation are derived using a non-homogeneous Markov process. The design is simple to implement and results in simple and easy to calculate estimators and variances. It generalizes maxima nomination sampling for use in finite populations and includes some other sampling designs as special cases. We provide some optimality results and show that, in the context of finite population sampling, maxima nomination sampling is not generally the optimum design to follow. We also show, through numerical examples and a case study, that the proposed design can result in significant improvements in efficiency compared to simple random sampling without replacement designs for a wide choice of population types. Finally, we describe a bootstrap method for choosing values of the design parameters.

Control charts for attributes with maxima nominated samples

We develop quality control charts for attributes using the maxima nomination sampling (MNS) method and compare them with the usual control charts based on simple random sampling (SRS) method, using average run length (ARL) performance, the required sample size in detecting quality improvement, and non-existence region for control limits. We study the effect of the sample size, the set size, and nonconformity proportion on the performance of MNS control charts using ARL curve. We show that MNS control chart can be used as a better benchmark for indicating quality improvement or quality deterioration relative to its SRS counterpart. We consider MNS charts from a cost perspective. We also develop MNS attribute control charts using randomized tests. A computer program is designed to determine the optimal control limits for an MNS p-chart such that, assuming known parameter values, the absolute deviation between the ARL and a specific nominal value is minimized. We provide good approximations for the optimal MNS control limits using regression analysis. Theoretical results are augmented with numerical evaluations. These show that MNS based control charts can yield substantial improvement over the usual control charts based on SRS.

Improved attribute acceptance sampling plans based on maxima nomination sampling

This paper demonstrates the use of maxima nomination sampling (MNS) technique in design and evaluation of single AQL, LTPD, and EQL acceptance sampling plans for attributes. We exploit the effect of sample size and acceptance number on the performance of our proposed MNS plans using operating characteristic (OC) curve. Among other results, we show that MNS acceptance sampling plans with smaller sample size and bigger acceptance number perform better than commonly used acceptance sampling plans for attributes based on simple random sampling (SRS) technique. Indeed, MNS acceptance sampling plans result in OC curves which, compared to their SRS counterparts, are much closer to the ideal OC curve. A computer program is designed which can be used to specify the optimum MNS acceptance sampling plan and to show, visually, how the shape of the OC curve changes when parameters of the acceptance sampling plan vary. Theoretical results and numerical evaluations are given.

A unified approach to variations of ranked set sampling with applications

In this article, we develop a general theory of inference using data collected from different variations of ranked set sampling. Such variations include balanced and unbalanced ranked set sampling, balanced and unbalanced k-tuple ranked set sampling, nomination sampling, simple random sampling, as well as a combination of them. We provide methods of estimating the underlying distribution function as well as its functionals and establish the asymptotic properties of the resulting estimators. The results so obtained can be used to develop nonparametric procedures for one- and two-sample problems. Some investigation of the small-sample properties of these estimators is also provided. We conclude with an application to a real-life example.

Asymptotic Properties of Nomination Sampling

Asymptotic Properties of Nomination Sampling

Influence of nurse gender on the use of silence, touch and humour.

A combination of data gathering approaches, i.e. conversation, observation and narrative exchange, were used to study the beliefs and actions of exemplary nurses. The data were analyzed using hermeneutic phenomenology and grounded theory methods and the findings revealed three major themes: dialogue in silence, mutual touch and sharing the lighter side of life. Participants in the study were chosen by peer nomination and reputational sampling and included both genders. The results showed a contrast in the way that exemplary males and females used silence, touch and humour in their practice. More specifically, compared with the women in the group, the men used silence to achieve different purposes, tended towards non-physical touch and used different forms of humour. This paper presents an introductory examination of the influence of nurse gender on the use of silence, touch and humour.