Imperfect Ranking Research Articles

Estimating the prevalence of osteoporosis using ranked-based methodologies and Manitoba's population-based BMD registry

Osteoporosis is a metabolic bone disorder that is characterized by reduced bone mineral density (BMD) and deterioration of bone microarchitecture. Osteoporosis is highly prevalent among women over 50, leading to skeletal fragility and risk of fracture. Early diagnosis and treatment of those at high risk for fracture is very important in order to avoid morbidity, mortality and economic burden from preventable fractures. The province of Manitoba established a BMD testing program in 1997. The Manitoba BMD registry is now the largest population-based BMD registry in the world, and has detailed information on fracture outcomes and other covariates for over 160,000 BMD assessments. In this paper, we develop a number of methodologies based on ranked-set type sampling designs to estimate the prevalence of osteoporosis among women of age 50 and older in the province of Manitoba. We use a parametric approach based on finite mixture models, as well as the usual approaches using simple random and stratified sampling designs. Results are obtained under perfect and imperfect ranking scenarios while the sampling and ranking costs are incorporated into the study. We observe that rank-based methodologies can be used as cost-efficient methods to monitor the prevalence of osteoporosis.

Improved model fitting approaches under ranked set sampling schemes with application to forest data

In this paper, we address the problem of fitting probabilistic models based on several sampling designs that originated from the ranked set sampling (RSS) scheme. Although these sampling designs have been proved to be efficient and/or economical alternatives to simple random sampling (SRS) and RSS, the problem of model fitting still should be properly studied for a complete understanding of their advantages. In this study, we investigated the performance of eight RSS-based designs, among them the recently proposed modified neoteric RSS (Taconeli & Cabral, 2019), combined with six estimation methods in model fitting. Through extensive simulations, we could identify the combinations that provided higher efficiency. The simulated results showed that the RSS-based designs outperformed SRS in model fitting, whereas the Anderson-Darling and maximum product of spacings were the most efficient among the estimation methods. In addition, the Anderson-Darling and maximum product of spacings estimation, combined with the neoteric RSS design and its variants, allowed the highest efficiency under both perfectand imperfect ranking. Additional simulations based on real data set from a forest inventory corroborated these findings.

Parameter estimation of the Lomax distribution using genetic algorithm based on the ranked set samples

ABSTRACT Due to the importance of business process automation in industry, hyperautomation and Robotic Process Automation (RPA) attract increasing attention in the scientific field as well. Hyperautomation allows automation to do important tasks performed by business people by merging Artificial Intelligence (AI) technologies with RPA. Lomax distribution has been widely used in engineering science, service times, use and supply times of products in enterprise information systems, income and wealth data, business failure data, medical and biological science, life test and other fields. In this paper, the maximum likelihood estimation of unknown parameters of the Lomax distribution is considered using simple random sample, ranked set sample, median ranked set sample and extreme ranked set sample. Model parameters are estimated by the maximum likelihood estimation method based on Genetic Algorithm. An extensive Monte Carlo simulation study, considering perfect and imperfect ranking, is carried out in order to compare the performance of the genetic algorithm and classical optimisation method from ranked set sample-based designs with corresponding simple random sample estimators. Real-life data has been used to illustrate the application of the results obtained.

Evaluation of maximum likelihood procedures in ranked set sampling under imperfect ranking

Ranked set sampling (RSS) is a cost-efficient alternative to simple random sampling (SRS) when ranking small sets of population units is much simpler than effectively measuring them. Maximum likelihood estimation (MLE) in RSS is usually based on the restrictive assumption of perfect ranking, assuming that the sample units lead to order statistics. However, this procedure is not flexible and often produces highly biased estimators when ranking errors are present. To remedy these constraints, in this work we suggest and evaluate alternative MLE procedures for RSS: (i) MLE based on the perfect ranking assumption; (ii) MLE based on the SRS assumptions; (iii) a weighted estimator derived from (i) and (ii); (iv) the choice of (i) or (ii) by testing the null hypothesis of perfect ranking. We carried out extensive simulations to investigate the efficiency of each strategy, which allowed us to conclude that although (i) performed the best under perfect ranking, (ii-iv) are preferable under imperfect ranking. We have also evaluated a parametric bootstrap algorithm to obtain confidence intervals in RSS based on the suggested estimators. Two applications using data from age determination of fishes and anthropometric measures of athletes illustrate and corroborate our findings.

Confidence-Aware Active Feedback for Interactive Instance Search

Online relevance feedback (RF) is widely utilized in instance search (INS) tasks to further refine imperfect ranking results, but it often has low interaction efficiency. The active learning (AL) technique addresses this problem by selecting valuable feedback candidates. However, mainstream AL methods require an initial labeled set for a cold start and are often computationally complex to solve. Therefore, they cannot fully satisfy the requirements for online RF in interactive INS tasks. To address this issue, we propose a confidence-aware active feedback method (CAAF) that is specifically designed for online RF in interactive INS tasks. Inspired by the explicit difficulty modeling scheme in self-paced learning, CAAF utilizes a pairwise manifold ranking loss to evaluate the ranking confidence of each unlabeled sample. The ranking confidence improves not only the interaction efficiency by indicating valuable feedback candidates but also the ranking quality by modulating the diffusion weights in manifold ranking. In addition, we design two acceleration strategies, an approximate optimization scheme and a top-K search scheme, to reduce the computational complexity of CAAF. Extensive experiments on both image INS tasks and video INS tasks searching for buildings, landscapes, persons, and human behaviors demonstrate the effectiveness of the proposed method. Notably, in the real-world, large-scale video INS task of NIST TRECVID 2021, CAAF uses 25% fewer feedback samples to achieve a performance that is nearly equivalent to the champion solution. Moreover, with the same number of feedback samples, CAAF's mAP is 51.9%, significantly surpassing the champion solution by 5.9%. Code is available at https://github.com/nercms-mmap/caaf.

On kernel-based estimation of distribution function and its quantiles based on ranked set sampling

This paper proposes to use the convex combination of several kernel estimators based on the ranked set sampling (RSS) scheme for estimating the underlying distribution function to construct more efficient quantiles estimation. Several different estimators of quantile function based on the simple random sampling and ranked set sampling are provided. The variance and mean-squared error of the proposed estimators are derived as explicit forms. Theoretical derivation and an intensive simulation study are used to compare the performance of the proposed method with other methods in the literature. The effect of imperfect rankings on the performance of the proposed estimators is investigated. Real data example from the China Health and Nutrition Survey is used to illustrate our proposed approach. Some discussions using another two real data are presented. It observes that the proposed estimators have different behaviours with respect to symmetric and asymmetric distributions.

On the improvement of paired ranked set sampling to estimate population mean

Abstract In ecological and environmental sampling the quantification of units is either difficult or overly demanding in terms of the time, money, workload, it requires. For this reason efficient and cost-effective sampling methods need to be devised for data collecting. The most commonly used method for this purpose is the Ranked Set Sampling (RSS). In this paper, a sampling scheme called Improved Paired Ranked Set Sampling (IPRSS) is proposed to estimate the population mean. The performance of the proposed IPRSS is evaluated under perfect and imperfect rankings. A simulation study based on selected hypothetical distributions and a real-life data set showed that IPRSS is more precise than RSS, Paired RSS (PRSS) or Extreme RSS (ERSS).

Some Shrinkage estimators based on median ranked set sampling

In this study, some shrinkage estimators using a median ranked set sample in the presence of multicollinearity were studied. Initially, we constructed the multiple regression model using median ranked set sampling. We also adapted the Ridge and Liu-type estimators to these multiple regression model. To investigate the efficiency of these estimators, a simulation study was performed for a different number of explanatory variables, sample sizes, correlation coefficients, and error variances in perfect and imperfect ranking cases. In addition, these estimators were compared with other estimators that are based on ranked set sample using simulation study. It is shown that when the collinearity is moderate, Ridge estimator using median ranked set sample performs better than other estimators and when the collinearity increases, Liu-type estimator using median ranked set sample gets better than all other estimators do. When the collinearity is smaller than 0.95, ridge estimator based on median ranked set sample is more efficient than Liu-type estimator based on same sample. However, this threshold increases as the sample size increases and the number of explanatory variables decreases. In addition, real data example is presented to illustrate how collinearity affects the estimators under median ranked set sampling and ranked set sampling.

ON EXTROPY PROPERTIES AND DISCRIMINATION INFORMATION OF DIFFERENT STRATIFIED SAMPLING SCHEMES

Ranked set sampling (RSS) and some of its variants are sampling designs that are applied widely in different areas. When the underlying population contains different subpopulations, we can use stratified ranked set sampling (SRSS) which combines the advantages of stratification with RSS. In the present paper, we consider the information content of SRSS in terms of extropy measure. Some results using stochastic orders properties are obtained. The effect of imperfect ranking on discrimination information is analytically investigated. It is proved that discrimination information between the perfect SRSS and simple random sampling (SRS) data sets performs better than that of between the imperfect SRSS and SRS data sets.

Robust confidence intervals for a proportion using ranked-set sampling

We develop two new approximate confidence interval methods for estimating a population proportion using balanced ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper–Pearson-type interval. Both methods rely on a new maximum-likelihood-based method for estimating the proportions in the judgment strata when the overall proportion is given, and both can be computed even for large sample sizes.

On kernel-based quantile estimation using different stratified sampling schemes with optimal allocation

ABSTRACT The kernel-based estimators of a quantile function based on stratified samples of simple random sampling and ranked set sampling methods are proposed. The expectations and variances of the estimators are analytically obtained as well as their asymptotic distributions. Effect of imperfect ranking is considered in all analytically and numerically results. As theory and using a simulation study, it is shown that the estimator based on stratified ranked set sampling is more efficient than its counterpart on the basis of stratified simple random sampling. The simulation study is performed for three strata with small samples as well as large samples and for ten strata. Finally, the performance of the estimator is investigated by using China Health and Nutrition data set.

Estimation based on ranked set sampling for the two-parameter Birnbaum–Saunders distribution

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and non-parametric inference. In this paper, we consider RSS-based estimation for the two-parameter Birnbaum–Saunders (BS) distribution, which is widely used in reliability analysis. The estimation methods considered for comparison purposes were: maximum likelihood (ML), modified method of moments (MMM), maximum product of spacings (MPS), and Anderson–Darling (AD). The performance of the RSS-based estimators was evaluated through Monte Carlo simulations under both perfect and imperfect ranking assumptions. The bias, mean squared error, and mean integrated squared error were used as the criteria for comparison. The results revealed that the RSS-based estimators perform better than their simple random sampling (SRS) counterparts. The ML estimator performed the best under the perfect ranking assumption, while the MMM provided better performance for higher levels of imperfect ranking. Additional simulations based on data from a forest inventory corroborated our findings.

Estimation of the inequality indices based on the well-known rank-based sampling schemes

Using the simple random sampling (SRS) for collecting the income data may results poor estimators specially when the sample size is not enough large. Since under this circumstance, it may be difficult to obtain a representative subset from the income population based on SRS. Ranked set sampling (RSS) and its simplified versions overcome to this shortcoming. These sampling schemes work based on judgment ranking of the sample units. Moreover, the judgment post-stratification sampling (JPS) is also another rank-based sampling plan that can be considered as a competitor of RSS. This paper is organized in order to find the most appropriate sampling scheme among the SRS, RSS, JPS and some more, for estimating of some well-known inequality indices. Comparison of the estimators is carried out through a simulation study based on both perfect and imperfect ranking mechanisms. Results show that the suggested scheme is different for each inequality index. Finally, a real data set is analyzed.

Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data

Ranked set sampling (RSS) has been proved to be a cost-efficient alternative to simple random sampling (SRS). However, there are situations where some measurements are censored, which may not ensure the superiority of RSS over SRS. In this paper, the performance of the maximum likelihood estimators is examined when the data are assumed to follow a Power Lindley or a Weighted Lindley distribution, and are collected according to the original RSS or one of its two variations (the median and extreme RSS). An extensive simulation study, considering uncensored and right-censored data, and perfect and imperfect ranking, is carried out based on the two mentioned distributions in order to compare the performance of the maximum likelihood estimators from RSS-based designs with the corresponding SRS estimators. Two illustrations are presented based on real data sets. The first involves the lifetimes of aluminum specimens, while the second deals with the amount of spray mixture deposited on the leaves of apple trees.

Estimation of the system reliability for generalized inverse Lindley distribution based on different sampling designs

In this paper, we are interested in estimating stress-strength reliability when the distributions of stress and strength are independent generalized inverse Lindley (GIL) under different sampling designs, namely, simple random sampling (SRS), ranked set sampling (RSS) and percentile ranked set sampling (PRSS). In the context of parameter estimation, we use maximum likelihood (ML) methodology. The performance of the ML estimators of stress-strength reliability based on SRS, RSS and PRSS are compared via a Monte-Carlo simulation study for different parameter settings and sample sizes under the assumptions of perfect and imperfect ranking, respectively. At the end of the study, the insulin resistance data set is analyzed to implement the proposed methodologies.

Vücut Yağı Verisi Kullanılarak Sıralı Küme Örneklemesine Dayalı Dağılım Fonksiyonu Kestiricilerinin Performansları

In this study, an application of empirical distribution function (EDF) estimators based on ranked set sampling (RSS) using real-life data set (body fat data) is illustrated. In this application, three variables which are percentage of body fat (Y), abdomen circumference (X1) and age (X2) are used. Age and abdomen circumference are separately used in ranking process as auxiliary variables which have correlation 0.813 (for perfect ranking) and 0.291 (for imperfect ranking) with the percentage of body fat, respectively. Ranked set samples are constructed by using three different sampling designs which are level-0 level-1 and level-2. The effects of perfect and imperfect ranking on the estimators of the sampling designs are investigated. Relative efficiencies of the EDF estimators are obtained by using their mean squared errors (MSE) and integrated mean squared errors (IMSE), numerically. For both perfect and imperfect ranking, these EDF estimators based on sampling designs have outperformance against EDF estimator based on SRS.

Using ranked set sampling with binary outcomes in cluster randomized designs

AbstractWe study the use of ranked set sampling (RSS) with binary outcomes in cluster‐randomized designs (CRDs), where a generalized linear mixed model (GLMM) is used to model the hierarchical data structure involved. Under the GLMM‐based framework, we propose three different approaches to estimate the treatment effect, including the nonparametric (NP), maximum likelihood (ML) and pseudo likelihood (PL) estimators. We investigate their asymptotic properties and examine their finite‐sample performance via simulation. Based on these three RSS estimators, we further develop procedures for testing the existence of the treatment effect. We examine the power and size of our proposed RSS tests and compare them with existing tests based on simple random sampling (SRS). All the proposed RSS estimation and test methods are illustrated with two data examples, one for rare events and the other for non‐extreme events. Throughout our investigations, we also consider the possible effect of imperfect ranking. Among the proposed methods, we provide recommendations on whether to use RSS rather than SRS with binary outcomes in CRDs and, if yes, when to use which RSS method. The Canadian Journal of Statistics 48: 342–365; 2020 © 2019 Statistical Society of Canada

Mixture ranked set sampling for estimation of population mean and median

ABSTRACTIn this paper, a sampling scheme named ‘mixture ranked set sampling’ (MIRSS) for estimation of the population mean and median is suggested. The MIRSS is applicable when the ordinary RSS cannot be fully conducted in all cycles of the experiment. We show that when the underlying distribution is symmetric, MIRSS provides unbiased estimator of population mean. Moreover, unbiased estimator of population variances is derived. A simulation study is conducted to evaluate the performance of the estimators under suggested scheme for both perfect and imperfect ranking. Our simulation results showed that the proposed scheme is more efficient than the extreme ranked set sampling (ERSS) and simple random sampling (SRS). In addition, the MIRSS is more efficient than ordinary RSS design when ranking is not perfect. The suggested scheme is also illustrated using real data set.

Mallows’ models for imperfect ranking in ranked set sampling

In this paper, we consider some statistical measures of deviation from the perfect ranking in the framework of ranked set sampling. We use nonparametric approach for testing the null hypothesis for perfect ranking. The distance-based Mallows’ models with appropriate distance on permutations are suggested in the case of imperfect ranking. Some asymptotic results for the corresponding error probability matrix are derived for the models based on Spearman’s footrule and Spearman’s rho. We propose an EM algorithm for estimating the unknown parameter in the Mallows’ models in order to compare the power of the presented test statistics.

Empirical distribution function estimators based on sampling designs in a finite population using single auxiliary variable

ABSTRACT In this paper, we study empirical distribution function (EDF) estimators based on ranked set sampling (RSS). Ranked set samples are constructed by using three different sampling designs which are level-0, level-1 and level-2. These designs are different in terms of their replacement policies. The sample is constructed by sampling with replacement in level-0 sampling design. In level-1 sampling design, the sample is constructed by sampling with replacement of the unmeasured units in each set. Also, we construct the sample without replacement on the entire set in level-2 sampling design. In simulation study, we compare EDF estimators when using sampling designs with EDF estimator when using simple random sampling (SRS) in finite populations having different distribution functions. The effects of both perfect and imperfect ranking on the estimators of the sampling designs are investigated. Relative efficiencies of the EDF estimators are obtained by using their integrated mean squared errors (IMSEs), numerically. For illustrative purposes, these EDF estimators based on sampling designs are applied to a real data set. By using both the simulation data and real data, we show that these EDF estimators have higher efficiencies against EDF based on SRS.