Bayesian subset selection approach to ranking normal means

In this, article we consider a Bayesian approach to the problem of ranking the means of normal distributed populations, which is a common problem in the biological sciences. We use a decision-theoretic approach with a straightforward loss function to determine a set of candidate rankings. This loss function allows the researcher to balance the risk of not including the correct ranking with the risk of increasing the number of rankings selected. We apply our new procedure to an example regarding the effect of zinc on the diversity of diatom species.     

New imperfect rankings models for ranked set sampling

Ranked set sampling is a sampling approach that leads to improved statistical inference in situations where the units to be sampled can be ranked relative to each other prior to formal measurement. This ranking may be done either by subjective judgment or according to an auxiliary variable, and it need not be completely accurate. In fact, results in the literature have shown that no matter how poor the quality of the ranking, procedures based on ranked set sampling tend to be at least as efficient as procedures based on simple random sampling. However, efforts to quantify the gains in efficiency for ranked set sampling procedures have been hampered by a shortage of available models for imperfect rankings. In this paper, we introduce a new class of models for imperfect rankings, and we provide a rigorous proof that essentially any reasonable model for imperfect rankings is a limit of models in this class. We then describe a specific, easily applied method for selecting an appropriate imperfect rankings model from the class.     

A New Conjoint Analysis Procedure with Application to Marketing Research

Abstract

In this article we propose some extensions and applications of the nonparametric combination of dependent rankings (see Pesarin, F., Lago, A. (2000). Nonparametric combination of department rankings with applications to the quality assessment of industrial products. Metron LVIII (1–2):39–52.) This methodology is applied to Conjoint Analysis in order to aggregate (ex ante) preferences from a group of individuals. Furthermore, a new global association test (GAT) is introduced in order to test for the association of the global ranking with all attributes of interest. The GAT procedure allows the experimenter to have clear indications on significant attributes by considering the intensity of the optimal weights given by the procedure itself. This may help the experimenter in interpreting the usual analysis involving the normal plot for detecting active effects.     

A Bayesian multiple comparison procedure for ranking the means of normally distributed data

We present a Bayesian decision-theoretic model for producing, via all pair-wise comparisons, a set of possible rankings for a given number of normal means. A simulation is performed to compare this constant loss model to popular frequentist methods used to rank normal means, including Tukeys method and the Benjamini–Hochberg procedure. The model will also be compared to a Bayesian model using a linear loss function. Properties to be compared include the probability of containing the true ranking and the expected number of possible rankings produced.     

Rank aggregation using latent-scale distance-based models

Rank aggregation aims at combining rankings of a set of items assigned by a sample of rankers to generate a consensus ranking. A typical solution is to adopt a distance-based approach to minimize the sum of the distances to the observed rankings. However, this simple sum may not be appropriate when the quality of rankers varies. This happens when rankers with different backgrounds may have different cognitive levels of examining the items. In this paper, we develop a new distance-based model by allowing different weights for different rankers. Under this model, the weight associated with a ranker is used to measure his/her cognitive level of ranking of the items, and these weights are unobserved and exponentially distributed. Maximum likelihood method is used for model estimation. Extensions to the cases of incomplete rankings and mixture modeling are also discussed. Empirical applications demonstrate that the proposed model produces better rank aggregation than those generated by Borda and the unweighted distance-based models.

     

Are Overall Journal Rankings a Good Mapping for Article Quality in Specialty Fields?

Overall journal rankings, which are generated with sample articles in different research fields, are commonly used to measure the research productivity of academic economists. In this article, we investigate a growing concern in the profession that the use of the overall journal rankings to evaluate scholars’ relative research productivity may exhibit a downward bias toward researchers in some specialty fields if their respective field journals are under-ranked in the overall journals rankings. To address this concern, we constructed new journal rankings based on the intellectual influence of research in 8 specialty fields using a sample consisting of 26,401 articles published across 60 economics journals from 1998 to 2007. We made various comparisons between the newly constructed journal rankings in specialty fields and the traditional overall journal ranking. Our results show that the overall journal ranking provides a considerably good mapping for the article quality in specialty fields. Supplementary materials for this article are available online.     

Finding the maximum efficiency for multistage ranked-set sampling

Multistage ranked-set sampling (MRSS) is a generalization of ranked-set sampling in which multiple stages of ranking are used. It is known that for a fixed distribution under perfect rankings, each additional stage provides a gain in efficiency when estimating the population mean. However, the maximum possible efficiency for the MRSS sample mean relative to the simple random sampling sample mean has not previously been determined. In this paper, we provide a method for computing this maximum possible efficiency under perfect rankings for any choice of the set size and the number of stages. The maximum efficiency tends to infinity as the number of stages increases, and, for large numbers of stages, the efficiency-maximizing distributions are symmetric multi-modal distributions where the number of modes matches the set size. The results in this paper correct earlier assertions in the literature that the maximum efficiency is bounded and that it is achieved when the distribution is uniform.     

Testing for a Trend in Partial Rankings

A test based on Spearman's footrule is proposed of the null hypothesis that several partial rankings are chosen randomly and uniformly from the set of all possible partial rankings. The alternative is that rankings are biased due to order of the objects. This test is similar to the Fligner and Verducci test for complete rankings.     

Estimating the distribution function using k-tuple ranked set samples

The basic assumption underlying the concept of ranked set sampling is that actual measurement of units is expensive, whereas ranking is cheap. This may not be true in reality in certain cases where ranking may be moderately expensive. In such situations, based on total cost considerations, k-tuple ranked set sampling is known to be a viable alternative, where one selects k units (instead of one) from each ranked set. In this article, we consider estimation of the distribution function based on k-tuple ranked set samples when the cost of selecting and ranking units is not ignorable. We investigate estimation both in the balanced and unbalanced data case. Properties of the estimation procedure in the presence of ranking error are also investigated. Results of simulation studies as well as an application to a real data set are presented to illustrate some of the theoretical findings.     

大学综合排名竞争策略研究——基于网大（www．netbig．com）大学排行榜的实证分析

关于提升大学综舍排名的竞争策略，可以运用累积Logit模型来研究各评价指标排名对大学综合排名的影响效应，通过提高那些对综合排名影响效应较大的指标排名，能更有效地促进综合排名的提高，从而确定有效的排名竞争策略。利用网大（www．netbig．com）“中国大学排行榜”的排名数据进行实证分析，得出排名越靠前的大学通过提升“声誉”和“学术成果”名次能最有效提升综合排名。而排名越靠后的大学则通过提升“学术资源”和“物资资源”名次能最有效提升综合排名等结论。     

A nonparametric procedure for testing partially ranked data

In consumer preference studies, it is common to seek a complete ranking of a variety of, say N, alternatives or treatments. Unfortunately, as N increases, it becomes progressively more confusing and undesirable for respondents to rank all N alternatives simultaneously. Moreover, the investigators may only be interested in consumers’ top few choices. Therefore, it is desirable to accommodate the setting where each survey respondent ranks only her/his most preferred k (k?N) alternatives. In this paper, we propose a simple procedure to test the independence of N alternatives and the top-k ranks, such that the value of k can be predetermined before securing a set of partially ranked data or be at the discretion of the investigator in the presence of complete ranking data. The asymptotic distribution of the proposed test under root-n local alternatives is established. We demonstrate our procedure with two real data sets.     

Accounting for clinical covariates and interactions in ranking genomic markers using ROC

In biomedical research, profiling is now commonly conducted, generating high-dimensional genomic measurements (without loss of generality, say genes). An important analysis objective is to rank genes according to their marginal associations with a disease outcome/phenotype. Clinical-covariates, including for example clinical risk factors and environmental exposures, usually exist and need to be properly accounted for. In this study, we propose conducting marginal ranking of genes using a receiver operating characteristic (ROC) based method. This method can accommodate categorical, censored survival, and continuous outcome variables in a very similar manner. Unlike logistic-model-based methods, it does not make very specific assumptions on model, making it robust. In ranking genes, we account for both the main effects of clinical-covariates and their interactions with genes, and develop multiple diagnostic accuracy improvement measurements. Using simulation studies, we show that the proposed method is effective in that genes associated with or gene–covariate interactions associated with the outcome receive high rankings. In data analysis, we observe some differences between the rankings using the proposed method and the logistic-model-based method.     

Some useful nonparametric tests for ordered alternatives in randomized block experiments

Testing for ordered alternatives in randomized block designs has been a problem of interest for almost three decades (Jonckheere (1954)). Three classes of rank tests have evolved—tests based on “within-blocks” rankings (W-tests), tests based on “ranking after alignment” within blocks (RAA-tests), and tests based on “among-blocks” rankings (A-Tests). This paper focuses on the latter. A simplified version of the Skillings-Wolfe generalized Purl test (1977) is suggested and two very useful A-tests—a generalized Johnson-Mehrotra “Optimal contrast” procedure and a generalized Tryon-Hettmansperger rank test—are developed. These procedures are compared and contrasted with other recent competitors presented by Skllllngs and Wolfe (1978) and by Salama and Quade (1981).     

A note on ranked-set sampling using a covariate

Ranked-set sampling (RSS) and judgment post-stratification (JPS) use ranking information to obtain more efficient inference than is possible using simple random sampling. Both methods were developed with subjective, judgment-based rankings in mind, but the idea of ranking using a covariate has received a lot of attention. We provide evidence here that when rankings are done using a covariate, the standard RSS and JPS mean estimators no longer make efficient use of the available information. We first show that when rankings are done using a covariate, the standard nonparametric mean estimators in JPS and unbalanced RSS are inadmissible under squared error loss. We then show that when rankings are done using a covariate, nonparametric regression techniques yield mean estimators that tend to be significantly more efficient than the standard RSS and JPS mean estimators. We conclude that the standard estimators are best reserved for settings where only subjective, judgment-based rankings are available.     

Ranked set sampling for ordered categorical variables

The authors show how ranked set sampling, both balanced and unbalanced, can be extended to ordered categorical variables with the goal of estimating the probabilities of all categories. They use ordinal logistic regression to aid in the ranking of the ordinal variable of interest. They also propose an optimal allocation scheme and methods for implementing it under either perfect or imperfect rankings. Results from a simulation study using data from the third National Health and Nutrition Examination Survey indicate that the use of ordinal logistic regression in ranking leads to substantial gains in precision for estimation of cell probabilities.     

Estimating the asymptotic relative efficiency of weighted rankings

Five tests for the hypothesis of no treatment effects in complete blocks designs are compared with respect to asymptotic relative efficiency: the ordinary two-way analysis of variance, the analysis of variance of ranks (Friedman, 1937), the method of ranking after alignment (Hodges and Lehmann, 1962), and a method of weighted rankings proposed by Quade (1972, 1979). This comparison required devising a procedure for estimating the asymptotic relative efficiencies of test statistics with asymp-totic chi-squared distributions.     

Concordance of Complete or Right-Censored Rankings Based on Spearman's Footrule

A right-censored ranking is what results when a judge ranks only the “top K” of M objects. Complete uncensored rankings constitute a special case. We present two measures of concordance among the rankings of N ≥ 2 such judges, both based on Spearman's footrule. One measure is unweighted, while the other gives greatest weight to the first rank, less to the second, and so on. We consider methods for calculating or estimating the P-values of the corresponding tests of the hypothesis of random ranking.     

Best linear unbiased and invariant estimation in location-scale families based on double-ranked set sampling

Abstract

In this article, we propose the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the unknown parameters of location-scale family of distributions based on double-ranked set sampling (DRSS) using perfect and imperfect rankings. These estimators are then compared with the BLUEs and BLIEs based on ranked set sampling (RSS). It is shown that under perfect ranking, the proposed estimators are uniformly better than the BLUEs and BLIEs obtained via RSS. We also propose the best linear unbiased quantile (BLUQ) and the best linear invariant quantile (BLIQ) estimators for normal distribution under DRSS. It is observed that the proposed quantile estimators are more efficient than the BLUQ and BLIQ estimators based on RSS for both perfect and imperfect orderings.     

Analysis of mutual funds’ management styles: a modeling,ranking and visualizing approach

A method to rank mutual funds according to their investment style measured with respect to the returns of a reference portfolio (benchmark) is introduced. It is based on a style analysis model estimating a mutual fund portfolio composition as well as the benchmark one. Starting from such compositions, it computes a proximity measure based on the L ₁ or L ₂ norm to assess the similarity between each mutual fund portfolio returns and the benchmark returns as well as between the returns of each benchmark constituent and that of the corresponding mutual fund constituent. To this purpose the mean integrated absolute error and the mean integrated squared error are computed to derive both a global ranking of mutual fund management styles and partial rankings expressing the over- (under-) weighting of each portfolio constituent. A visual inspection of the results emphasizing main differences in management styles is provided, using a parallel coordinates plot. Since a modeling, a ranking and a visualizing approach are integrated, the method is named MoRaViA. From the practitioners’ point of view, it allows the identification of a specific management style for each mutual fund, discriminating active management funds from passive management ones. To evaluate the effectiveness of MoRaViA, many sets of artificial portfolios are generated and an application on a set of equity funds operating in the European market is presented.     

A statistical procedure for representing state fragility and transition paths

State fragility is a concept that entered the political discourse in the last decades producing remarkable implications for aid allocation and international policies. The operationalization of this concept has generated a number of composite indices to produce rankings of fragile states. However, the temporal dimension of the driving forces leading to fragility has been rather neglected. This article discusses a statistical procedure that helps to represent the global fragility of a country and the path that a country has followed or will follow in the future when possibly entering into (or escaping from) a fragility condition. Specifically, multiple factor analysis is applied to depict vulnerable and weak countries, and to identify the fundamental forces that determine their overall fragility. Moreover, the trajectories of countries along the years are estimated using partial factor scores. Finally, the path of each country is predicted by means of parsimonious regression models, based on a reduced set of explanatory variables, and according to scenarios elaborated from available international outlooks.