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Two-phase sampling is a useful technique for sample surveys, particularly when prior auxiliary data is not accessible. The ranks of the auxiliary variable often coincide with those of the research variable when two variables are correlated. By considering this relationship, we can significantly increase estimator accuracy. In this paper, we use the ranks of the auxiliary variable along with extreme values to estimate the population mean of the study variable. Up to a first-order approximation, we analyze the characteristics of the suggested class of estimators with an emphasis on biases and mean squared errors in stratified two-phase sampling. The theoretical results are verified using different datasets and a simulation study, which demonstrates that the proposed estimators outperform the existing ones in terms of percent relative efficiency. [ABSTRACT FROM AUTHOR]

In this paper we contribute towards the classification of partially symmetric tensors in F q 3 ⊗ S 2 F q 3 , q even, by classifying planes which intersect the Veronese surface V (F q) in at least one point, under the action of K ≤ PGL (6 , q) , K ≅ PGL (3 , q) , stabilising the Veronese surface. We also determine a complete set of geometric and combinatorial invariants for each of the orbits. [ABSTRACT FROM AUTHOR]

Outlier values and rankings are important for emphasizing data distribution variability, which improves the accuracy and effectiveness of variance estimations. To enhance the estimation of finite population variance in a two-phase sampling framework, this study presents an improved class of double exponential-type estimators by utilizing the outlier values and ranks of an auxiliary variable. A theoretical analysis is conducted to derive the biases and mean squared errors (MSEs) of these estimators using first-order approximations. A comprehensive simulation study is then performed to analyze the performance of the proposed estimators. The results clearly show that the new estimators provide more precise estimates, achieving a higher percentage relative efficiency (PRE) across all simulated scenarios. Furthermore, three data sets are analyzed to further confirm the efficiency of the proposed estimators as compared to other existing estimators. These results emphasize the potential of the proposed class of estimators to optimize variance estimation techniques, making it a more cost-effective and accurate choice for researchers using two-phase sampling in a variety of domains. [ABSTRACT FROM AUTHOR]

In this research paper, an improved set of estimators for finding the finite population variance of a study variable under a stratified two-phase sampling design is introduced. These estimators rely on information about extreme values and the ranks of an auxiliary variable. We examined the properties of these estimators using first-order approximation, focusing on biases and mean squared errors (MSEs). Additionally, we conducted an extensive simulation study to evaluate their performance and validate our theoretical insights. Furthermore, in the application section, we employed some datasets to further assess the performances of our estimators as compared to other existing estimators. The results demonstrated that $ S^2_{Q_2} $ was the best-performing estimator, and significantly outperforms existing estimators, achieving a percent relative efficiency $ (PRE) $ in the exponential distribution as high as 385.467. The percent relative efficiency values were continuously higher than 100 in a variety of situations, with values as high as 353.129 in other distributions like the uniform and gamma. The suggested estimators are superior to the conventional estimators, as demonstrated by empirical assessments using datasets, where percent relative efficiency improvements ranged from 115.026 to 139.897. These results highlight the robustness and applicability of the proposed class of estimators in real-world sampling.

Multiple primary endpoints are commonly used in randomized controlled trials to assess treatment effects. When the endpoints are measured on different scales, the O'Brien rank‐sum test or the Wei–Lachin test for stochastic ordering may be used for hypothesis testing. However, the O'Brien–Wei–Lachin (OWL) approach is unable to handle missing data and adjust for baseline measurements. We present a nonparametric approach for data analysis that encompasses the OWL approach as a special case. Our approach is based on quantifying an endpoint‐specific treatment effect using the probability that a participant in the treatment group has a better score than (or a win over) a participant in the control group. The average of the endpoint‐specific win probabilities (WinPs), termed the global win probability (gWinP), is used to quantify the global treatment effect, with the null hypothesis gWinP = 0.50. Our approach involves converting the data for each endpoint to endpoint‐specific win fractions, and modeling the win fractions using multivariate linear mixed models to obtain estimates of the endpoint‐specific WinPs and the associated variance–covariance matrix. Focusing on confidence interval estimation for the gWinP, we derive sample size formulas for clinical trial design. Simulation results demonstrate that our approach performed well in terms of bias, interval coverage percentage, and assurance of achieving a pre‐specified precision for the gWinP. Illustrative code for implementing the methods using SAS PROC RANK and PROC MIXED is provided. [ABSTRACT FROM AUTHOR]

We derive a local formula for the parity of the 2 ∞ -Selmer rank of Jacobians of curves of genus 2 or 3 which admit an unramified double cover. We give an explicit example to show how this local formula gives rank parity predictions against which the 2-parity conjecture may be tested. Our results yield applications to the parity conjecture for semistable curves of genus 3. [ABSTRACT FROM AUTHOR]

In this research paper, an improved set of estimators for finding the finite population variance of a study variable under a stratified two-phase sampling design is introduced. These estimators rely on information about extreme values and the ranks of an auxiliary variable. We examined the properties of these estimators using first-order approximation, focusing on biases and mean squared errors (MSEs). Additionally, we conducted an extensive simulation study to evaluate their performance and validate our theoretical insights. Furthermore, in the application section, we employed some datasets to further assess the performances of our estimators as compared to other existing estimators. The results demonstrated that S Q 2 2 was the best-performing estimator, and significantly outperforms existing estimators, achieving a percent relative efficiency (P R E) in the exponential distribution as high as 385.467. The percent relative efficiency values were continuously higher than 100 in a variety of situations, with values as high as 353.129 in other distributions like the uniform and gamma. The suggested estimators are superior to the conventional estimators, as demonstrated by empirical assessments using datasets, where percent relative efficiency improvements ranged from 115.026 to 139.897. These results highlight the robustness and applicability of the proposed class of estimators in real-world sampling. [ABSTRACT FROM AUTHOR]

Ranks of partitions play an important role in the theory of partitions. They provide combinatorial interpretations for Ramanujan's famous congruences for partition functions. We establish a family of congruences modulo powers of $5$ for ranks of partitions. [ABSTRACT FROM AUTHOR]

A nonparametric method proposed by DeLong et al in 1988 for comparing areas under correlated receiver operating characteristic curves is used widely in practice. However, the DeLong method as implemented in popular software quietly deletes individuals with any missing values, yielding potentially invalid and/or inefficient results. We simplify the DeLong algorithm using ranks and extend it to accommodate missing data by using a mixed model approach for multivariate data. Simulation results demonstrate the validity and efficiency of our procedure for data missing at random. We illustrate our proposed procedure in SAS, Stata, and R using the original DeLong data. [ABSTRACT FROM AUTHOR]

To estimate the finite population variance of the study variable, this paper proposes an improved class of efficient estimators using different transformations. When both the minimum and maximum values of the auxiliary variable are known and the ranks of the auxiliary variable are associated with the study variable, these estimators are particularly useful. Therefore, the precision of the estimators can be effectively improved through the utilization of these rankings. We examine the properties of the proposed class of estimators, including bias and mean squared error (MSE), using a first-order approximation through a stratified random sampling method. To determine the performances and validate the findings mathematically, a simulation study is carried out. Based on the results, the proposed class of estimators performs better in terms of the mean squared error (M S E) and percent relative efficiency (P R E) as compared to other estimators in all scenarios. Furthermore, in order to prove that the performances of the improved class of estimators are better than those of the existing estimators, three data sets are examined in the application section. [ABSTRACT FROM AUTHOR]

This article presents a new set of estimators designed to estimate the finite population variance of a study variable in two-phase sampling. These estimators utilize the information about extreme values and ranks of an auxiliary variable. Through a first-order approximation, we investigate the properties of these estimators, including biases and mean squared errors (MSEs). Furthermore, a comprehensive simulation study is conducted to assess their performance and validate our theoretical insights. Results demonstrate that our proposed class of estimators performs better in terms of percent relative efficiency (PRE) across various simulation scenarios compared to existing estimators. In addition, in the application section, we utilize three data sets to further validate the performance of our proposed estimators against conventional unbiased variance estimators, ratio and regression estimators, as well as other existing methods. [ABSTRACT FROM AUTHOR]

This article suggests an improved class of efficient estimators that use various transformations to estimate the finite population variance of the study variable. These estimators are particularly helpful in situations where we know about the minimum and maximum values of the auxiliary variable, and the ranks of the auxiliary variable are associated with the study variable. Consequently, these rankings can be applied as an effective tool to improve the accuracy of the estimator. A first-order approximation is used to investigate the properties of the proposed class of estimators, such as bias and mean squared error ( M S E ) under simple random sampling. A simulation study carried out in order to measure the performance and verify the theoretical results. The suggested class of estimators has a greater percent relative efficiency ( P R E ) than the other existing estimators in all of the simulated situations, according to the results. Three symmetric and asymmetric datasets are examined in the application section in order to show the superior performance of the proposed class of estimators over the existing estimators. [ABSTRACT FROM AUTHOR]

Copyright of Cuadernos de Investigación Geográfica is the property of Universidad de la Rioja, Servicio de Publicaciones and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This website proposes comprehensive information about educational scope and possibilities in the Arts, Science, and Commerce streams. This platform serves as a dynamic hub where students can explore various academic options, empowering them to make well–informed decisions about their educational journey.It mainly aims toward career scope in Arts, Science, and Commerce, Entrance exams that are available for engineering degrees, and different engineering courses available in India. Prospective students can easily search for institutions based on factors such as location, field of study, admission criteria, and more. Additionally, information about scholarships, entrance exams, and application procedures streamlines the often complex and overwhelming process of applying to colleges and universities. It is an education based website with college prediction using machine learning algorithm like linear regression and random forest with Tkinter library. EduVerse main aim is to help students to get information about the courses, entrance exam, scholarships and colleges’ admission criteria and all this thing at one place is the main motive of this website. Our application “EduVerse” is aimed to help students understand and know all the career opportunities and to make confident choices about their educational pursuits. [ABSTRACT FROM AUTHOR]

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics of randomly growing permutations. Permutations connect total orders on a finite set, which leads to the use of a pattern frequencies. This view is closely related to classical concepts of nonparametric statistics. We give several applications and discuss related topics and research areas, in particular the treatment of other combinatorial families, the cycle view of permutations, and an approach via exchangeability. [ABSTRACT FROM AUTHOR]

It is often desired to rank different populations according to the value of some feature of each population. For example, it may be desired to rank neighbourhoods according to some measure of intergenerational mobility or countries according to some measure of academic achievement. These rankings are invariably computed using estimates rather than the true values of these features. As a result, there may be considerable uncertainty concerning the rank of each population. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each population. We consider both the problem of constructing marginal confidence sets for the rank of a particular population as well as simultaneous confidence sets for the ranks of all populations. We show how to construct such confidence sets under weak assumptions. An important feature of all of our constructions is that they remain computationally feasible even when the number of populations is very large. We apply our theoretical results to re-examine the rankings of both neighbourhoods in the U.S. in terms of intergenerational mobility and developed countries in terms of academic achievement. The conclusions about which countries do best and worst at reading, math, and science are fairly robust to accounting for uncertainty. The confidence sets for the ranking of the fifty most populous commuting zones by measures of mobility are also found to be small. These confidence sets, however, become much less informative if one includes all commuting zones, if one considers neighbourhoods at a more granular level (counties, census tracts), or if one uses movers across areas to address concerns about selection. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Wildland Fire Science is the property of Journal of Wildland Fire Science Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We develop a novel exploratory tool for non-Euclidean object data based on data depth, extending celebrated Tukey's depth for Euclidean data. The proposed metric halfspace depth, applicable to data objects in a general metric space, assigns to data points depth values that characterize the centrality of these points with respect to the distribution and provides an interpretable center-outward ranking. Desirable theoretical properties that generalize standard depth properties postulated for Euclidean data are established for the metric halfspace depth. The depth median, defined as the deepest point, is shown to have high robustness as a location descriptor both in theory and in simulation. We propose an efficient algorithm to approximate the metric halfspace depth and illustrate its ability to adapt to the intrinsic data geometry. The metric halfspace depth was applied to an Alzheimer's disease study, revealing group differences in the brain connectivity, modeled as covariance matrices, for subjects in different stages of dementia. Based on phylogenetic trees of seven pathogenic parasites, our proposed metric halfspace depth was also used to construct a meaningful consensus estimate of the evolutionary history and to identify potential outlier trees. for this article are available online. [ABSTRACT FROM AUTHOR]

We prove that for any fixed k$$ k $$, the probability that a random vertex of a random increasing plane tree is of rank k$$ k $$, that is, the probability that a random vertex is at distance k$$ k $$ from the leaves, converges to a constant ck$$ {c}_k $$ as the size n$$ n $$ of the tree goes to infinity. We prove that 1−∑j≤kck<22k+3(2k+4)!$$ 1-{\sum}_{j\le k}{c}_k<\frac{2^{2k+3}}{\left(2k+4\right)!} $$, so that the tail of the limiting rank distribution is super‐exponentially narrow. We prove that the latter property holds uniformly for all finite n$$ n $$ as well. More generally, we prove that the ranks of a finite uniformly random set of vertices are asymptotically independent, each with distribution {ck}$$ \left\{{c}_k\right\} $$. We compute the exact value of ck$$ {c}_k $$ for 0≤k≤3$$ 0\le k\le 3 $$, demonstrating that the limiting expected fraction of vertices with rank ≤3$$ \le 3 $$ is 0.9997$$ 0.9997 $$... We show that with probability 1−n−0.99ε$$ 1-{n}^{-0.99\varepsilon } $$ the highest rank of a vertex in the tree is sandwiched between (1−ε)logn/loglogn$$ \left(1-\varepsilon \right)\log n/\mathrm{loglog}n $$ and (1.5+ε)logn/loglogn$$ \left(1.5+\varepsilon \right)\log n/\mathrm{loglog}n $$, and that this rank is asymptotic to logn/loglogn$$ \log n/\mathrm{loglog}n $$ with probability 1−o(1)$$ 1-o(1) $$. [ABSTRACT FROM AUTHOR]

Introduction. The paper provides a first historiographic insight into official ranks and social status of Russian diplomats to have been dispatched on diplomatic missions to leaders of nomadic military/political associations across Northern Central Asia in the 17th century. Goals. The study aims to determine essentials of how the Tsardom of Russia tended to perceive its counterparties’ status through the analysis of official positions and social backgrounds of Russian diplomats. Materials and methods. The article analyzes a wide range of published and unpublished documents, systemizes and generalizes qualitative and quantitative data pertaining to official ranks of Russian diplomats discovered in records management papers, such as Tsar’s ukazes, nakazes and reminder nakazes, as well as those referred to as stateyny spisok (list of officers) and otpiska voevody (governor’s report). Results. The work reveals diplomatic missions to Kirghiz and Teleut lands, Dzungaria and Mongolia were usually headed by offsprings of the nobility (deti boyarskie) and regular servicemen (nachalnye lyudi) — Cossack leaders, atamans, squadron (pyatidesyatnik) and section (desyatnik) commanders. However, it was not that rare when such diplomatic endeavors were entrusted to servicemen of lower ranks and, occasionally, representatives of indigenous (non-Russian) populations. Conclusions. In terms of 16th–17th century Russian ambassadorial semiotics, the choice of diplomats from commoners and those characterized by lower social status was definitely purposeful and aimed at demonstrating that Turkic and Mongolian nomadic rulers were to enjoy fewer honors due to a higher standing of the Russian Tsar. Since the Tsardom of Muscovy was seeking to gain control over the nomadic military/political alliances of Northern Central Asia and bring nomadic elites under ‘the higher hand of the monarch’, the appointments of lower-ranked servicemen as heads of diplomatic missions were to meet the goals (and logic) of Russian expansionist policy. Low ranks of dispatched diplomats indicated not only the Russian Tsar’s political superiority over nomadic rulers but also attested to that Russians already tended to perceive nomads as potential subjects of the Tsar.

The growth of Artificial Intelligence applications requires to develop risk management models that can balance opportunities with risks. We contribute to the development of Artificial Intelligence risk models proposing a Rank Graduation Box (RGB), a set of integrated statistical metrics that can measure the "Sustainability", "Accuracy", "Fairness" and "Explainability" of any Artificial Intelligence application. Our metrics are consistent with each other, as they are all derived from a common underlying statistical methodology: the Lorenz curve. The validity of the metrics is assessed by means of their practical application to both simulated and real data. The results from the comparison of alternative machine learning models to simulated data are aligned with the generating models, in general indicating linear regression models as the most accurate, regression tree models as the most fair, Random Forest models as the most robust; and leading to model explanations similar to the true ones from the generating model. The outcomes from the application of Random Forest models to real data show that the proposed RGB metrics are more interpretable and more consistent with the expectations, with respect to standard metrics such as AUC, RMSE and Shapley values. The evidence also shows that the RGB metrics are very general and can be applied to any machine learning method, regardless of the underlying data and model. • A new toolkit for evaluating the trustworthiness condition of AI systems. • Our method is based on the use of the Lorenz and concordance curves. • The metrics provide a measure of the compliance AI applications as a percentage. • The application shows the suitability of the approach for assessing AI methods. [ABSTRACT FROM AUTHOR]

Atkin and Garvan introduced the functions N k (n) and M k (n) , which denote the k -th moments of ranks and cranks in the theory of partitions. Let e 2 r (n) be the n -th Fourier coefficient of E 2 r (τ) / η (τ) , where E 2 r (τ) is the classical Eisenstein series of weight 2 r and η (τ) is the Dedekind eta function. Via the theory of quasi-modular forms, we find that for k ≤ 5 , N k (n) and M k (n) can be expressed using e 2 r (n) (0 ≤ r ≤ k), p (n) and N 2 (n). For k > 5 , additional functions are required for such expressions. For r ∈ { 2 , 3 , 4 , 5 , 7 } , by studying the action of Hecke operators on E 2 r (τ) / η (τ) , we provide explicit congruences modulo arbitrary powers of primes for e 2 r (n). Moreover, for ℓ ∈ { 5 , 7 , 11 , 13 } and any k ≥ 1 , we present uniform methods for finding nice representations for ∑ n = 0 ∞ e 2 r ( ℓ k n + 1 24) q n , which work for every r ≥ 2. These representations allow us to prove congruences modulo powers of ℓ , and we have done so for e 4 (n) and e 6 (n) as examples. Based on the congruences satisfied by e 2 r (n) , we establish congruences modulo arbitrary powers of ℓ for the moments and symmetrized moments of ranks and cranks as well as higher order spt-functions. [ABSTRACT FROM AUTHOR]

Copyright of ESPOCH Congresses: The Ecuadorian Journal of S.T.E.A.M. is the property of Knowledge E DMCC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the present paper, we consider the semigroup On,p of all order-preserving full transformations α on an n-elements chain Xn, where p ∈ Xn is the only fixed point of α. The nilpotent semigroup On,p was first studied by Ayik et al. in 2011. Moreover, On,1 is the maximal nilpotent subsemigroup of the Catalan Monoid Cn. Its rank is the difference of the (n - 1) th and the (n - 2) th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup On,p. We will calculate the rank of On,p for p > 1 and provide a semigroup presentation for On,1. [ABSTRACT FROM AUTHOR]

This paper introduces tests for the symmetry of the copula of random vector. The proposed statistics are based on the copula characteristic function and the weight function that appears naturally in their definition are assumed to belong to the general family of Lévy measures. The proposed test statistics are rank‐based and expresses as weighted L2‐norms computed from a vector of empirical copula characteristic functions. Their nondegenerate asymptotic distributions under the null hypothesis and general alternatives, as well as the validity of a multiplier bootstrap for the computation of p‐values, are derived using nonstandard arguments. Extended Monte–Carlo experiments show that the new tests hold their size well and are powerful against a wide range of alternatives, and appear to be more powerful than a Cramér–von Mises test based on empirical copulas. [ABSTRACT FROM AUTHOR]

In the survey sampling, when the study and auxiliary variables are tolerably correlated, the ranks of an auxiliary variable also relate mutually with the study variable and thus by using these ranks as a valid mechanism, increases the accuracy of an estimator. In the current study, an enhanced estimator of the finite population mean is proposed that uses the ancillary information in form of the ranks of the auxiliary variable in stratified sampling design. Simulated as well as empirical evidence is provided for the efficiency confirmation of proposed estimators. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodology that combines standard production theory with Multiple-Criteria Decision Analysis (MCDA) methods to rank banks based on their capability of using investment in new technologies to reduce the other inputs' usage, for a given level of output. Banks are first ranked based on their investment in innovation (innovation rank); afterwards, we calculate the overall rank by combining two factors of production, viz. labor and assets, using the PROMETHEE II approach that belongs to the family of the outranking methods. We then use directional efficiency measures to measure the banks' efficiency by means of relation between two ranks, for a given level of the outputs. We apply the methodology to a sample of US and EU banks sourced from Orbis BankFocus. The key findings suggest there are four types of banks in our sample: (a) banks whose innovation rank is positively correlated with the overall rank; (b) banks exhibiting a negative correlation between two ranks: their overall ranks are low while still exhibiting high innovation ranks; (c) banks with high overall rank but low innovation rank and (d) banks with the worst ranks both for the innovation rank and the overall rank. The least efficient banks belong to this group.

This article introduces a two-step calibration technique for the inverse relationship between study variable and auxiliary variable along with the double use of the auxiliary variable. In the first step, the calibration weights and design weights are set proportional to each other for a given sample. While in the second step, the constant of proportionality is to be obtained on the basis of some different objectives of the investigation viz. bias reduction or minimum Mean Squared Error (MSE) of the proposed estimator. Many estimators based on inverse relationship between x and y have been already developed and are considered to be special cases of the proposed estimator. Properties of the proposed estimator is discussed in details. Moreover, a simulation study has also been conducted to compare the performance of the proposed estimator under Simple Random Sampling Without Replacement (SRSWOR) and Lahiri-Midzuno (L-M) sampling design in terms of percent relative bias and MSE. The benefits of two-step calibration estimator are also demonstrated using real life data. [ABSTRACT FROM AUTHOR]

Permutation tests based on previously developed statistics are proposed for the case of mixed paired and two-sample designs. Different weighting schemes of previous tests are explored to understand the strengths and weaknesses of each test. A simulation study compares the power and Type I error rates of the new tests with those previously developed. Rank-based statistics generally performed as well as or better than parametric statistics, particularly for nonnormal distributions. [ABSTRACT FROM AUTHOR]

Many popular nonparametric inferential methods are based on ranks. Among the most commonly used and most famous tests are for example the Wilcoxon-Mann-Whitney test for two independent samples, and the Kruskal-Wallis test for multiple independent groups. However, recently, it has become clear that the use of ranks may lead to paradoxical results in case of more than two groups. Luckily, these problems can be avoided simply by using pseudo-ranks instead of ranks. These pseudo-ranks, however, suffer from being (a) at first less intuitive and not as straightforward in their interpretation, (b) computationally much more expensive to calculate. The computational cost has been prohibitive, for example, for large-scale simulative evaluations or application of resampling-based pseudorank procedures. In this paper, we provide different algorithms to calculate pseudo-ranks efficiently in order to solve problem (b) and thus render it possible to overcome the current limitations of procedures based on pseudo-ranks.

Copyright of College of Law Journal for Legal & Political Sciences / Magallat Kulliyyat Al-Qanun Li-L-ulum Al-Qanuniyyat Wa-Al-Siyasiyyat is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The definitions of the rank and crank for overpartitions were given by Bringmann, Lovejoy and Osburn. Let N ¯ (s , l ; n) (resp. M ¯ (s , l ; n) , M 2 ¯ (s , l ; n) ) denote the number of overpartitions of n with rank (resp. the first residual crank, the second residual crank) congruent to s modulo l. The rank differences of overpartitions modulo 3, 5, 6, 7 and 10 were determined. In this paper, we establish the generating functions for N ¯ (s , l ; n) , M ¯ (s , l ; n) and M 2 ¯ (s , l ; n) with l = 4 , 8 by utilizing Appell–Lerch sums and theta function identities. Moreover, in light of these generating functions, we obtain some equalities and inequalities on ranks and cranks of overpartitions modulo 4 and 8. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Duzce University Institute of Social Sciences / Düzce Üniversitesi Sosyal Bilimler Dergisi is the property of Duzce University Journal of Social Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article attempts to estimate the size of the wage premia fetched by ranked academics on the academic market in Ústí nad Labem, Czechia. We employed a large (anonymized) data set of contracts and wages of employees of a medium-sized regional public university in Ústí nad Labem. We used OLS regression in various specifications to determine the wage premia of all educational levels (mainly full professors over associate professors/ docents and associate professors/docents over assistant professors/PhDs) while controlling for many attributes (of employees or contracts) possibly affecting wage levels. The local context regarding the topic of this article is discussed as well. The results generally confirm the intuition and show a clear pattern of increasing wages with levels and ranks. Focusing predominantly on the academic ranks, the monthly premium of associate professors (docents) over PhDs seems to be somewhere between 5 and 6 thousand CZK (185 and 220 EUR), and the premium of full professors over associate professors to an average of around 4 thousand CZK (150 EUR). The latter premium, however, exhibits systematic variation across different schools within the university: in some it is insignificant (around 0), while in others it is rather large and averages around 8 thousand CZK (300 EUR). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider wavelet analysis to obtain an estimator of a copula function based on censored data. We show that optimal convergence rates for the mean integrated squared error (MISE) of linear wavelet-based function estimators are exact under right censoring model. Moreover, we derive asymptotic formulae for MISE. Finally, the simulation results and the analysis of real data validate the proposed procedure.

Copyright of Ma'alim Quran Sunnah is the property of Universiti Sains Islam Malaysia (USIM) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

It is well known that the least squares estimate in classical linear regression model is very sensitive to violation of the assumptions, in particular normality of model errors. That is why a lot of alternative estimates has been developed to overcome these shortcomings. Quite interesting class of such estimates is formed by R-estimates. They use only ranks of response variable instead of their actual value. The goal of this paper is to extend this class by another estimates and tests based only on ranks. First, we will introduce a new rank test in linear regression model. The test statistic is based on a certain minimum distance estimator, but unlike classical rank tests in regression it is not a simple linear rank statistic. Then, we will return back to estimates and generalize minimum distance estimates for various type of distances. We will show that in some situation these tests and estimates have greater power than the classical ones. Theoretical results will be accompanied by a simulation study to illustrate finite sample behavior of estimates and tests.

The present article investigates issues of military terminology in the Hungarian and Romanian subtitles of the highly popular TV mini-series Band of Brothers. The introductory part offers a brief presentation of terms, possible definitions, and their relevance for translators/subtitlers, and then – based on a possible mind map of military terms, including army units, equipment, ranks, commands, tactics, rewards, and punishments – we analyse samples belonging to army equipment and ranks (commanders) in the Hungarian and Romanian subtitles, arguing for the importance of reliable sources and consistency, which directly contribute to the quality of translations or subtitles. A special field of investigation may be represented by the specific military abbreviations and acronyms, which may offer an objective insight into the level of expertise of the translators/subtitlers.

We present a permutation bootstrap method for reducing the variance of estimation in the so-called block maxima (BM) method in extreme value theory. In the case of independent and identically distributed observations, it is sensible to use the permutation bootstrap to reduce the variance of the parameter and quantile estimators. The method is analyzed and we propose an implementation of the permutation bootstrap based on a particular sampling from the data based on the BM-ranks whose distribution is derived and easy to simulate. The performance of the method is discussed in a numerical study on simulated and then real data. [ABSTRACT FROM AUTHOR]

Computational representation of everyday emotional states is a challenging task and, arguably, one of the most fundamental for affective computing. Standard practice in emotion annotation is to ask people to assign a value of intensity or a class value to each emotional behavior they observe. Psychological theories and evidence from multiple disciplines including neuroscience, economics and artificial intelligence, however, suggest that the task of assigning reference-based values to subjective notions is better aligned with the underlying representations. This paper draws together the theoretical reasons to favor ordinal labels for representing and annotating emotion, reviewing the literature across several disciplines. We go on to discuss good and bad practices of treating ordinal and other forms of annotation data and make the case for preference learning methods as the appropriate approach for treating ordinal labels. We finally discuss the advantages of ordinal annotation with respect to both reliability and validity through a number of case studies in affective computing, and address common objections to the use of ordinal data. More broadly, the thesis that emotions are by nature ordinal is supported by both theoretical arguments and evidence, and opens new horizons for the way emotions are viewed, represented and analyzed computationally. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop a measure for characterizing complex dependence between time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of functionals of the Fourier coefficients which is a generalization of coherence. Here, we use standard parametric copula models with a single parameter from both elliptical and Archimedean families. Our approach is to analyze changes in activity in local field potentials in the rat cortex prior to and immediately following the onset of stroke. We present the necessary theoretical background, the multivariate models and an illustration of our methodology on these local field potential data. Simulations with nonlinear dependent data reveal that there is information that is missed by not taking into account dependence on specific frequencies. Moreover, these simulations demonstrate how our proposed method captures more complex nonlinear dependence between time series. Finally, we illustrate our copula-based approach in the analysis of local field potentials of rats. [ABSTRACT FROM AUTHOR]