Ranked Set Research Articles

Sensitive proportion in ranked set sampling

This paper considers the concomitant-based rank set sampling (CRSS) for estimation of the sensitive proportion. It is shown that CRSS procedure provides an unbiased estimator of the population sensitive proportion, and it is always more precise than corresponding sample sensitive proportion (Warner SL (1965)) that based on simple random sampling (SRS) without increasing sampling cost. Additionally, a new estimator based on ratio method is introduced using CRSS protocol, preserving the respondent’s confidentiality through a randomizing device. The numerical results of these estimators are obtained by using numerical integration technique. An application to real data is also given to support the methods.

Another look at regression analysis using ranked set samples with application to an osteoporosis study.

Statistical learning with ranked set samples has shown promising results in estimating various population parameters. Despite the vast literature on rank-based statistical learning methodologies, very little effort has been devoted to studying regression analysis with such samples. A pressing issue is how to incorporate the rank information of ranked set samples into the analysis. We propose two methodologies based on a weighted least squares approach and multilevel modeling to better incorporate the rank information of such samples into the estimation and prediction processes of regression-type models. Our approaches reveal significant improvements in both estimation and prediction problems over already existing methods in the literature and the corresponding ones with simple random samples. We study the robustness of our methods with respect to the misspecification of the distribution of the error terms. Also, we show that rank-based regression models can effectively predict simple random test data by assigning ranks to them a posteriori using judgment poststratification. Theoretical results are augmented with simulations and an osteoporosis study based on a real data set from the Bone Mineral Density (BMD) program of Manitoba to estimate the BMD level of patients using easy to obtaincovariates.

On surfaces of minimal degree in [formula omitted

There are exactly four surfaces of minimal degree in P5, up to projective equivalence. And they have the same graded Betti numbers. So it is a natural question to ask how to recognize them by their defining equations. In this paper we provide an answer to this question in terms of the rank loci of quadratic equations of those four surfaces. We show that the sets of rank 3 and rank 4 quadratic equations distinguish them.

Efficient Estimation of the Generalized Quasi-Lindley Distribution Parameters under Ranked Set Sampling and Applications

Ranked set sampling is a very useful method to collect data when the actual measurement of the units in a population is difficult or expensive. Recently, the generalized quasi-Lindley distribution is suggested as a new continuous lifetime distribution. In this article, the ranked set sampling method is considered to estimate the parameters of the generalized quasi-Lindley distribution. Several estimation methods are used, including the maximum likelihood, the maximum product of spacings, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling methods. The performance of the proposed ranked set sampling based estimators is achieved through a simulation study in terms of bias and mean squared errors compared to the simple random sample. Additional results are obtained based on real data for the survival times of 72 guinea pigs and 23 ball bearings. The simulation study results and the real data applications showed the superiority of the proposed ranked set sampling estimators compared to the simple random sample competitors based on the same number of measuring units.

Beyond pairwise comparisons in social choice: A setwise Kemeny aggregation problem

In this paper, we advocate the use of setwise contests for aggregating a set of input rankings into an output ranking. We propose a generalization of the Kemeny rule where one minimizes the number of k-wise disagreements instead of pairwise disagreements (one counts 1 disagreement each time the top choice in a subset of alternatives of cardinality at most k differs between an input ranking and the output ranking). After an algorithmic study of this k-wise Kemeny aggregation problem, we introduce a k-wise counterpart of the majority graph. This graph reveals useful to divide the aggregation problem into several sub-problems, which enables to speed up the exact computation of a consensus ranking. By introducing a k-wise counterpart of the Spearman distance, we also provide a 2-approximation algorithm for the k-wise Kemeny aggregation problem. We conclude with numerical tests.

Bayesian Estimation of Morgenstern Type Bivariate Rayleigh Distribution Using Some Types of Ranked Set Sampling

In this paper we consider Bayesian estimation based on bivariate ranked set sample, in which units are ranked based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We obtain Bayes estimator for the scale parameter of the study variate Y, when (X, Y ) follows a Morgenstern type bivariate Rayleigh distribution. The Bayes estimators are considered based on bivari-ate ranked set sampling, extreme ranked set sampling and maximum ranked set sampling with unequal sample. The accuracy of estimation methods in this paper is illustrated using simulation study. Finally, a real data set is analyzed.

Estimation of ordinal population with multi-observer ranked set samples using ties information

In many surveys, we often deal with situations where measuring the study variable is expensive; however, there are easy-to-measure characteristics which can be used as ranking information to obtain more representative samples from the population. Ranked set sampling is successfully employed in these cases as an alternative to commonly used simple random sampling. When the data is ordinal categorical, it is common to apply the ordinal logistic regression approach to ranked set sampling data for the estimation of parameters. This technique first depends on the information of training data. Besides, one is not capable of using the ranking information in the estimation process. In this paper, we propose a ranked set sampling scheme in which ranking information from multiple sources can be combined and incorporated efficiently into both data collection and estimation. The ranked set sampling data is used for non-parametric and maximum likelihood estimation of ordinal categorical population. Through extensive simulation studies, the performance of estimators is evaluated. The methods are finally applied to analyze bone disorder data and obesity data.

AN ANALYSIS OF INFORMATION SYSTEMS RESEARCHER AND COLLABORATION RANKINGS

ABSTRACT This paper investigates a career database with a ranking of researchers, over the time period 1960–2019 based on a composite measure of Scopus citations, using the H-index, H-M-index and other metrics. This paper drills down on those researchers for which information systems is characterized as their primary focus. In so doing we investigate issues, related to collaboration and other concerns. In addition, the paper compares that set of rankings to a set of rankings for information systems researchers based on Google Scholar H-index, which allows us to compare Scopus H-index, Scopus H-M index and other analytics for those researchers.

Inference for Linear Exponential Distribution Based on Record Ranked Set Sampling

Inference for Linear Exponential Distribution Based on Record Ranked Set Sampling

Bayesian Inference for the Parameters of Kumaraswamy Distribution via Ranked Set Sampling

In this paper, we address the estimation of the parameters for a two-parameter Kumaraswamy distribution by using the maximum likelihood and Bayesian methods based on simple random sampling, ranked set sampling, and maximum ranked set sampling with unequal samples. The Bayes loss functions used are symmetric and asymmetric. The Metropolis-Hastings-within-Gibbs algorithm was employed to calculate the Bayes point estimates and credible intervals. We illustrate a simulation experiment to compare the implications of the proposed point estimators in sense of bias, estimated risk, and relative efficiency as well as evaluate the interval estimators in terms of average confidence interval length and coverage percentage. Finally, a real-life example and remarks are presented.

Fairness and the set of optimal rankings for the linear ordering problem

Fairness and the set of optimal rankings for the linear ordering problem

Efficient, robust and effective rank aggregation for massive biological datasets

Massive biological datasets are available in various sources. To answer a biological question (e.g., “which are the genes involved in a given disease?”), life scientists query and mine such datasets using various techniques. Each technique provides a list of results usually ranked by importance (e.g., a list of ranked genes). Combining the results obtained by various techniques, that is, combining ranked lists of elements into one list of elements is of paramount importance to help life scientists make the most of various results and prioritize further investigations. Rank aggregation techniques are particularly well-fitted with this context as they take in a set of rankings and provide a consensus, that is, a single ranking which is the “closest” to the input rankings. However, (i) the problem of rank aggregation is NP-hard in most cases (using an exact algorithm is currently not possible for more than a few dozens of elements) and (ii) several (possibly very different) exact solutions can be obtained. As answer to (i), many heuristics and approximation algorithms have been proposed. However, heuristics cannot guarantee how far from an exact solution the consensus ranking will be, and the approximation ratio of approximation algorithms dedicated to the problem is fairly high (not less than 3/2). No solution has yet been proposed to help true-users dealing with the problem encountered in point (ii).In this paper we present a complete system able to perform rank aggregation of massive biological datasets. Our solution is efficient as it is based on an original partitioning method making it possible to compute a high-quality consensus using an exact algorithm in a large number of cases. Our solution is robust as it clearly identifies for the user groups of elements whose relative order is the same in any optimal solution. These features provide answers to points (i) and (ii) and lie in mathematical bases offering guarantees on the computed result. Also, our solution is effective as it has been implemented into a real tool, ConquR-BioV2 is used for the life science community, and evaluated at large-scale using a very large number of datasets.

Ranking Sets of Defeasible Elements in Preferential Approaches to Structured Argumentation: Postulates, Relations, and Characterizations

Preferences play a key role in computational argumentation in AI, as they reflect various notions of argument strength vital for the representation of argumentation. Within central formal approaches to structured argumentation, preferential approaches are applied by lifting preferences over defeasible elements to rankings over sets of defeasible elements, in order to be able to compare the relative strength of two arguments and their respective defeasible constituents. To overcome the current gap in the scientific landscape, we give in this paper a general study of the critical component of lifting operators in structured argumentation. We survey existing lifting operators scattered in the literature of argumentation theory, social choice, and utility theory, and show fundamental relations and properties of these operators. Extending existing works from argumentation and social choice, we propose a list of postulates for lifting operations, and give a complete picture of (non-)satisfaction for the considered operators. Based on our postulates, we present impossibility results, stating for which sets of postulates there is no hope of satisfaction, and for two main lifting operators presented in structured argumentation, Elitist and Democratic, we give a full characterization in terms of our postulates.

Memory type ratio and product estimators under ranked-based sampling schemes

The exponential weighted moving average (EWMA) statistic is utilized the past information along with the present to enhance the efficiency of the estimators used for estimating the population parameters. In this study, the EWMA statistic is used for the estimation of population mean with suitable auxiliary information. The memory type ratio and product estimators are proposed under ranked-based sampling (RBS) schemes including extreme ranked set sampling, median ranked set sampling, and quartile ranked set sampling. The expressions of mean square errors (MSE) of the proposed estimators are derived. An extensive simulation study is conducted to evaluate the performance of the proposed estimators. An empirical study is presented based on real-life data that supports the findings of the simulation study.

A New Application of Generalized Linear Failure Rate Distribution in Agriculture Using Ranked Set Sampling

Abstract This article deals with perform inferences about stress–strength model R=P[Y<X] when X and Y are two independent random variables with generalized linear failure rate distribution (GLFRD) with the same and known scale parameters but not identically shaped parameters. In the literature, estimators based on simple random sample (SRS) are widely used in estimating stress–strength model. But in the resent years, ranked set sampling (RSS) has become popular in performing statistical inference. Therefore, the estimator of R based on RSS using maximum likelihood and modified maximum likelihood are obtained. Monte Carlo simulation study is performed to compare the estimators of R are obtained using RSS and SRS. Finally, agriculture application is presented.

Cumulative residual extropy of minimum ranked set sampling with unequal samples

Recently, an alternative measure of uncertainty called cumulative residual extropy (CREX) was proposed by Jahanshahi et al. (2019). In this paper, we consider uncertainty measures of minimum ranked set sampling procedure with unequal samples (MinRSSU) in terms of CREX and its dynamic version and we compare the uncertainty and information content of CREX based on MinRSSU and simple random sampling (SRS) designs. Also, using simulation, we study new estimators of CREX for MinRSSU and SRS designs in terms of bias and mean square error. Finally, we provide a new discrimination measure of disparity between the distribution of MinRSSU and parental data SRS.

A highly scalable algorithm for weak rankings aggregation

• Fast and scalable algorithms to deal with optimal bucket order problem. • First ordering then append (FOTA) approach. • Comparison with counterpart approach (first clustering then ordering). • Sound experimental evaluation including benchmarks with very large datasets. The Optimal Bucket Order Problem (OBOP) is a rank aggregation problem which consists in finding a consensus ranking (with ties) that generalizes a set of input rankings. In this paper, with the aim of solving the OBOP in an efficient and scalable way, we propose several greedy algorithms based on different sort-first and cluster-second strategies. More specifically, the sorting step is based on the Borda method, whereas in the cluster step, pairs of adjacent buckets are suitably joined. The proposed methods are experimentally compared with the state-of-the-art greedy algorithms for solving the OBOP by using a large benchmark of real-world databases. Furthermore, we provide a complete statistical analysis of the experimental study, which shows that several of the proposed algorithms outperform the current state-of-the-art greedy algorithms. We also analyze the trade-off between accuracy and execution time of the algorithms to guide the users regarding the selection of the best option for each particular case. The study carried out shows that our proposal is not only competitive in terms of accuracy with the state-of-the-art evolutionary strategy for dealing with the OBOP, but is also fast and scalable.

A new application of R = P[Y < X] for the inverse Lindley distribution using ranked set sampling

In this paper, we consider the problem of performing inference about reliability parameter R = P[Y < X] based on ranked set sampling (RSS) when the distribution of stress Y and strength X are inverse Lindley. The point estimator of R based on (RSS) using maximum likelihood method is obtained. In context of interval estimation an asymptotic confidence interval (ACI) and bootstrap confidence interval (BCI) are derived for R based on (RSS). The effectiveness of the proposed estimator is indicated in simulation study which compare the proposed estimators by their corresponding based on simple random sample (SRS). Finally a real data in medicine is used to illustrate our proposed estimators.

On developing sensitive nonparametric mixed control charts with application to manufacturing industry

AbstractControl charts are designed under the normality assumption of the quality characteristic of the process. However, the normality assumption rarely holds in practice. In non‐normal conditions, parametric charts tend to display more false alarm rates and invalid out‐of‐control comparisons. The exponentially weighted moving average chart is a frequently used memory‐type control chart for monitoring the process target that only performs effectively under the smoothing parameter's small choices. This study proposes a nonparametric mixed exponentially weighted moving average‐progressive mean chart based on sign statistic (NPMEPSN) under simple and ranked set sampling schemes to address this said drawback. Normal and non‐normal distributions are included in this study to observe the proposed chart's in‐control behavior and out‐of‐control efficacy. The prominent feature of the proposed schemes is that it works efficiently in detecting small and persistent shifts in the process location corresponding to the given values of the smoothing parameter. The proposed scheme is also tested under the ranked set sampling scheme to enhance the NPMEPSN chart's performance (hereafter named “NPMEPRSN”). The performance of the proposed charts is investigated through simulations using run‐length profiles. The proposed schemes were seen to outperform other alternatives, specifically under the ranked set sampling scheme. A real data‐set related to the diameter of a piston ring is included as a demonstration of the proposal.

Fisher Information in Moving Extreme Ranked Set Sampling with Application to Parameter Estimation

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling (MERSS) is considered for the Fisher information matrix for the location-scale family. The Fisher information matrix for this model are respectively derived under simple random sampling and MERSS. In order to give more insight into the performance of MERSS with respect to simple random sampling, the Fisher information matrix for usual location-scale distributions are respectively computed under the two sampling. The numerical results show that MERSS provides more information than simple random sampling in parametric inference.