Nonmetric Data Research Articles

ПАЛЕОАНТРОПОЛОГИЧЕСКАЯ СПРАВКА ПО ПОГРЕБЕНИЮ ИЗ ЯБЛОНОВО-4

The article gives a brief paleoanthropological characteristic of an individual from the archaeological heritage site Yablonovo-4 settlement, Lipetsk Oblast, Russia. The site dates back to the Middle Ages. The craniological (Alekseev&Debets), osteological (Alekseev) and dental metric and nonmetric data (Zubov&ASUDAS) of an adult male, 25–30 years old is presented. According to the study, the individual has a brachycranic skull. Most of the measurements of the skull fall into average category by Alekseev&Debets. The long bones are massive; the dental morphology traits of the Yablonovo 4 individual tend to be like the ones of the Western odontological stock (Zubov classification).

Craniological and Dental Non-Metric Data on the Origin of the Early Iron Age Gorokhovo Culture Population

The article is devoted to the research of craniological and dental non-metric data from Sargat and Gorokhovo burials. Gorokhovo Culture groups were located in the Upper and Middle Iset and Middle Tobol River regions in 6th–3rd cc BC. The research examines the anthropological uniqueness of the population of the Gorokhovo Culture and the racial and genetic processes that occurred in the forest-steppe territory in the south of Western Siberia in the Early Iron Age. It was established that the sample of the Gorokhovo Culture can be classified as Caucasian populations with a small Mongoloid admixture. Two Caucasian combinations of characteristics have been identified. The morphotype with a narrower and higher face profiled horizontally, a higher nose bridge and a larger angle of protrusion of the nasal bones in retrospect may be associated with groups of Andronovo-Alakul people; later this complex was represented as part of the Sauromatian-Sarmatian population of the European part of Russia. Found in the West Siberian Gorokhovo population it may be due to migration influence. Another Caucasoid component with a lower and wider slightly flattened facial skeleton, a less protruding nose and bridge of the nose is in many ways similar to the morphotype of the AndronovoFedorovo, and the later Sargat population. In this case we can talk about the autochthony origin. Dental nonmetric data organically complements the current results. Dental non-metric traits results demonstrates that the basis of the anthropological composition of the Gorokhovo population was the Andronovo component of South Ural origin. The population of the Sargat culture and the Gorokhovo groups who lived at the same time in the Tobol River Region in the 5th–3rd cc BC differ significantly. However, close population ties between the Sargat and Gorokhovo and their contacts with the Sarmatians contributed to the convergence of their anthropological structure.

Two-Level Dynamic Programming-Enabled Non-Metric Data Aggregation Technique for the Internet of Things

The Internet of Things (IoT) has become a transformative technological infrastructure, serving as a benchmark for automating and standardizing various activities across different domains to reduce human effort, especially in hazardous environments. In these networks, devices with embedded sensors capture valuable information about activities and report it to the nearest server. Although IoT networks are exceptionally useful in solving real-life problems, managing duplicate data values, often captured by neighboring devices, remains a challenging issue. Despite various methodologies reported in the literature to minimize the occurrence of duplicate data, it continues to be an open research problem. This paper presents a sophisticated data aggregation approach designed to minimize the ratio of duplicate data values in the refined set with the least possible information loss in IoT networks. First, at the device level, a local data aggregation process filters out outliers and duplicates data before transmission. Second, at the server level, a dynamic programming-based non-metric method identifies the longest common subsequence (LCS) among data from neighboring devices, which is then shared with the edge module. Simulation results confirm the approach’s exceptional performance in optimizing the bandwidth, energy consumption, and response time while maintaining high accuracy and precision, thus significantly reducing overall network congestion.

Craniological and dental non-metric data on the problem of the interaction between the repre-sentatives of the Sargatka and Bolsherechenskaya Cultures of the forest-steppe of the south Western Siberia

In the present paper, fully based on previously published craniological and dental non-metric data, the origins of common morpho-logical elements in the compositions of representatives of the Sargatka and Bolsherechenskaya Cultures are investigated. An attempt is made to assess the available data with the aid of the integrated analysis, implying combined examination of craniological and dental non-metric data for each population. The previous studies of the craniological and dental non-metric data showed that the series are significantly distinct in the differentiation by the vector ‘west-east’, or, in other words, Caucasoidness-Mongoloidness. Despite this, their certain affinity was recorded repeatedly, both in the analysis of craniometric data as well as in the study of odontoscopic data, but no explanation of this peculiarity has yet been proposed. The craniological sample of the Sargatka Culture comprised 158 crania and the dental non-metric one — 424 crania. The boundaries of the areal of the Sargatka Culture encompass the forest-steppe zone of the south of Western Siberia: the basins of the rivers Tobol, Ishim, and Irtysh, and the Baraba forest-steppe. The examined materials were divided in four groups corresponding to these territories. The craniological sample of the Bolsherechenskaya Culture comprised 118 crania, and the dental non-metric data amounted to 326 crania. The Bolsherechenskaya Culture materials originate from 11 burial grounds in the territory of the Novosibirsk Ob basin. All data were previously published. In the results, the population interaction of the bearers of the Sargat and Belsherechenskaya Cultures has been recorded, in which some representatives of the Kamenskaya Culture of the forest-steppe Altai were also involved, which is confirmed by archaeological data. However, it should be emphasized that this interaction was not so wide-scale. The Sargatka series, being located near to the Bolsherechenskaya ones, are also located in the same field with autochthonous Siberian groups. This becomes the evidence of the fact that not only the interaction in the Early Iron Age binds together the representa-tives of the Sargatka and Bolsherechenskaya Cultures. The fact is that the specificity of the anthropological composition of the Bolsherechenskaya people is directly related to the most ancient autochthonous Siberian populations, whereas the specific features of the Sargatka people — to southwestern migrants. However, an important result of the conducted analysis is that the composition of the Sargatka series retains the specific elements which are characteristic of the autochthonous populations of Western Siberia and which do not disappear under the influence of foreign migrant groups — this is the maturised structure of the lower molars.

Credibilistic Multi-Period Mean-Entropy Rolling Portfolio Optimization Problem Based on Multi-Stage Scenario Tree

This study considers a time-consistent multi-period rolling portfolio optimization issue in the context of a fuzzy situation. Rolling optimization with a risk aversion component attempts to separate the time periods and psychological effects of one’s investment in a mathematical model. Furthermore, a resilient portfolio selection may be attained by taking into account fuzzy scenarios. Credibilistic entropy of fuzzy returns is used to measure portfolio risk because entropy, as a measure of risk, is not dependent on any certain sort of symmetric membership function of stock returns and may be estimated using nonmetric data. Mathematical modeling is performed to compare the Rolling Model (RM) and the Unified Model (UM). Two empirical studies from the Tehran stock market (10 stocks from April 2017 to April 2019) and the global stock market (20 stocks from April 2021 to April 2023) are utilized to illustrate the applicability of the suggested strategy. The findings reveal that RM can limit the risk of the portfolio at each time, but the portfolio’s return is smaller than that of UM. Furthermore, the suggested models outperform the standard deterministic model.

Digitalization and Spatial Documentation of Post-Earthquake Temporary Housing in Central Italy: An Integrated Geomatic Approach Involving UAV and a GIS-Based System

Geoinformation and aerial data collection are essential during post-earthquake emergency response. This research focuses on the long-lasting spatial impacts of temporary solutions, which have persisted in regions of Central Italy affected by catastrophic seismic events over the past 25 years, significantly and permanently altering their landscapes. The paper analyses the role of geomatic and photogrammetric tools in documenting the emergency process and projects in post-disaster phases. An Atlas of Temporary Architectures is proposed, which defines a common semantic and geometric codification for mapping temporary housing from territorial to urban and building scales. The paper presents an implementation of attribute specification in existing official cartographic data, including geometric entities in a 3D GIS data model platform for documenting and digitalising these provisional contexts. To achieve this platform, UAV point clouds are integrated with non-metric data to ensure a complete description in a multiscalar approach. Accurate topographic modifications can be captured by extracting very high-resolution orthophotos and elevation models (DSM and DTM). The results have been validated in Visso (Macerata), a small historical mountain village in Central Italy which was heavily damaged by the seismic events of 2016/2017. The integrated approach overcomes the existing gaps and emphasizes the importance of managing heterogeneous geospatial emergency data for classification purposes. It also highlights the need to enhance an interoperable knowledge base method for post-disaster temporary responses. By combining geomatic tools with architectural studies, these visualization techniques can support national and local organizations responsible for post-earthquake management through a 3D modelling method to aid future transformations or interventions following other natural disasters.

A unifying framework for rank and pseudo-rank based inference using nonparametric confidence distributions

Nonparametric confidence distributions estimate statistical functionals by a distribution function on the parameter space, instead of the classical point or interval estimators. The concept bears analogy to the Bayesian posterior, but is nevertheless a completely frequentist concept. In order to ensure the desired statistical properties, we require that the cumulative distribution function on the parameter space is, evaluated at the true parameter, uniformly distributed over the unit interval. Our main focus lies on developing confidence distributions for the nonparametric relative effect and some natural extensions thereof. We develop asymptotic, range preserving and—especially important in the case of small sample sizes—approximate confidence distributions based on rank and pseudo-rank procedures. Due to the close relationship between point estimators, confidence intervals and p-values, these can all be approached in a unified manner within the framework of confidence distributions. The main goal of our contribution is to make the powerful theory of confidence distributions available in a nonparametric context, that is, for situations where methods relying on parametric assumptions are not justifiable. Application of the proposed methods and interpretation of the results is demonstrated using real data sets, including ordinal, non-metric data.

Comparing the performance of Kernel PCA Mix Chart with PCA Mix Chart for monitoring mixed quality characteristics

Along with the development of information and technology, the quality characteristics of a product cannot be monitored separately in the different types of control charts. In the past, conventional control charts were developed to monitor only one type of quality characteristic. The variable control charts are used to observe the variable or metric quality characteristics. Meanwhile, in monitoring non-metric characteristics or categorical data, attribute control charts are employed. To accommodate these two types of data, the PCA Mix control chart is suggested to simultaneously monitor these two types of data in one chart. However, some drawbacks occur when this chart is applied to monitor non-metric data which has an imbalanced proportion. Therefore, the Kernel PCA Mix control chart is created to overcome the gaps that occurred in the PCA Mix chart. Similar to the previous chart, this chart is also constructed using Hotelling’s T2 statistics with Kernel Density Estimation control limit. Several simulations are used to evaluate the performance of the proposed control charts. The simulation results show that the proposed chart has a better result than the previous control chart, especially for a small mean shift with an imbalanced proportion of non-metric data. However, the PCA Mix chart has a similar performance to the proposed chart when it is applied to monitor the balanced proportion of categorical data with a large mean shift. The application with simulated data with various scenarios and the real-world case also shows that the Kernel PCA Mix chart performs better compared to the performance of the PCA Mix chart.

Preservation of Villages in Central Italy: Geomatic Techniques’ Integration and GIS Strategies for the Post-Earthquake Assessment

Historical villages represent a highly vulnerable cultural heritage; their preservation can be ensured thanks to technological innovations in the field of geomatics and information systems. Among these, Geographical Information Systems (GISs) allow exploiting heterogeneous data for efficient vulnerability assessment, in terms of both time and usability. Geometric attributes, which currently are mainly inferred by visual inspections, can be extrapolated from data obtained by geomatic technologies. Furthermore, the integration with non-metric data ensures a more complete description of the post-seismic risk thematic mapping. In this paper, a high-performance information system for small urban realities, such as historical villages, is described, starting from the 3D survey obtained through the integrated management of recent innovative geomatic sensors, such as Unmanned Aerial Vehicles (UAVs), Terrestrial Laser Scanners (TLSs), and 360º images. The results show that the proposed strategy of the automatic extraction of the parameters from the GIS can be generalized to other case studies, thus representing a straightforward method to enhance the decision-making of public administrations. Moreover, this work confirms the importance of managing heterogeneous geospatial data to speed up the vulnerability assessment process. The final result, in fact, is an information system that can be used for every village where data have been acquired in a similar way. This information could be used in the field by means of a GIS app that allows updating the geospatial database, improving the work of technicians. This approach was validated in Gabbiano(Pieve Torina), a village in Central Italy affected by earthquakes in 2016 and 2017.

Foramen Ovale and Associated Accessory Foramina

Background: The mandibular nerve exits the cranial cavity by traversing through the foramen ovale (FO) which is located in the greater wing of sphenoid, posterolateral to foramen rotundum. This foramen also provides an entry portal to the accessory middle meningeal artery and helps exit the lesser petrosal nerve apart from the emissary veins. Tumors and masses in infratemporal region require an accurate and precise morphometry of FO, before planning any surgical procedure. The aim of this study is to record and analyze the metric and nonmetric data and compares the morphometry of FO with gender and age. Methodology: Type of study – Retrospective observational study. The sample size was 200 computerized tomography head axial section scans without any disease which might alter the anatomy of foramen, from picture archiving and communication system. Bilateral foraminal parameters were obtained with the help of computer-assisted software. Results: The mean length, breadth, distance from mid-sagittal plane, and size of FO in males were 7.75 ± 1.16, 3.98 ± 0.91, 21.40 ± 1.75, and 30.94 ± 8.79, and in females, measurements were 6.90 ± 0.78, 3.57 ± 1.04, 20.36 ± 1.62, and 24.86 ± 9.08, respectively. Septation was observed in 2% of cases and the most common shape observed was oval (84%). Totally 26% of accessory foramina were observed. Conclusion: Significant gender differences were seen in the morphometry in all the four parameters. A significant difference with age was seen only with distance of foramen from midsagittal plane. Variations in morphometry and shapes of the FO may affect clinical and diagnostic procedures.

Comparative analysis of metric and nonmetric aspects of foramen ovale of South Indian population with various regions globally and its approach through zygomatic route

Context: The foramen ovale is an obliquely placed, oval-shaped opening at the base of the skull in the greater wing of sphenoid. As the foramen transmits mandibular nerve, accessory meningeal artery, lesser petrosal nerve, and emissary veins, it knowledge of its variations is of supreme interest for surgeons. Aims: The aim of this study is to study the metric and nonmetric variations, of the foramen ovale of 40 dry adult human dried skulls. Settings and Design: The study was conducted in the dissection hall of Chettinad Academy of Research and Education. The study undertaken here is an observational study. Subjects and Methods: Human skulls were studied for location, patency, and various morphometric parameters bilaterally. The materials used were thin copper wire and a digital Vernier caliper of precision 0.01 mm. Statistical Analysis Used: Metric and nonmetric data were analyzed using the SPSS software. Results: The shape of foramen ovale was D shaped in most of the skulls (35%) followed by almond (21%), elongated oval (15%), and oval shape (11%). The presence of bony variations like spur was seen in 27.5% foramina, bony septa in 3.75%, and duplication in 21.25% foramina. The mean length and width of foramen ovale were 6.51 ± 1.24 mm and 3.66 ± 0.82 mm on right and 6.59 ± 1.33 mm and 3.75 ± 0.68 mm on the left, respectively. The mean area of foramen ovale was 19.08 ± 5.71 mm2 and 17.88 ± 5.85 mm2 on the right and the left, respectively. Conclusions: A sound knowledge on the morphometric variations of the foramen ovale helps the operating surgeon to avoid damage to the adjacent structures.

Research on Structural Flexibility and Acceptance Model (SFAM) Reconstruction Based on Disruption Innovation in the Social Humanities and Education Sector

The research objectives are as follows: (1) Developing a flexible structural model of the relationship between variables. (2) Develop a structural model that is robust with the assumptions of normality and homoscedasticity. (3) Obtain estimator properties from the flexible and robust SFAM structural model. (4) Obtaining hypothesis testing of each relationship constructed from a flexible and robust SFAM structural model. This research is integrated with a flexible and robust model approach based on nonparametric smoothing spline (RNSS) regression analysis which can capture the form of relationships that depend on empirical data, and the robustness of the model based on the distribution assumption and the assumption of homoscedasticity error variance. There are at least three transformation methods, namely SRS, MSI, and RASCH, which will be used in the development of the Structural Flexibility and Acceptance Model (SFAM). The results obtained from the research progress report are obtaining the development of a flexible structural model of the form of the relationship between variables, obtaining the development of a robust structural model of the assumptions of normality and homoscedasticity, obtaining the estimator properties of the flexible and robust SFAM structural model, and obtaining hypothesis testing. of each relationship constructed from a flexible and robust SFAM structural model. The originality of the theory in this study is very visible in the discovery of a new model, namely SFAM which can accommodate several things, which are the weaknesses of several existing analysis tools such as reciprocal and recursive models, more than one endogenous variable, flexible and robust models, overcoming inadmissible solutions, reflective indicators, formative , and reflective/formative (on the second-order), metric and non-metric data, and simultaneous processing of the input score data (through transformation to scale).

On the origin of the Early Iron Age Kashino population of Western Siberia (archaeological and dental non-metric data evidence)

In this study, based on the analysis of the dental characteristics of the series from the burial ground Abatsky-3 (III–V centuries AD) we considered the questions of the origin of the Kashin population of Western Siberia of the early Iron Age. Despite the small number of the studied sample (16 individuals), the detailed morphological characteristics and the results of multivariate statistical analysis made it possible to clarify a number of hypotheses about the origins and relationships of the Early Iron Age Kashino population of Western Siberia. The specificity of the Kashino population from the Abatsky-3 burial ground lies in a high predominance of the “Eastern” dental non-metric complex, namely, in the high frequencies of the 6-cusps lower molars, the distal trigonid crest, and, to a lesser extent, the deflecting wrinkle on the first lower molars. This complex of characteristics clearly differentiates this population from the groups of the Bronze Age and the Early Iron Age of Western Siberia and adjacent territories. According to the results of our study, it can be assumed that populations of the Kashino and Sargat cultures (latter is the closest to the representatives of the Kashino culture in the territorial and cultural terms) have different origin and their contacts were based more on cultural rather than population interactions. The results of the analysis favor to the hypothesis of the penetration of the Kama population related to the Ananyino and Glyadenovo cultures into the Trans-Urals and suggest the contribution of the Ananyino groups in the formation of the Kashino population.

Relationship of Oncotype Dx score with tumor grade, size, nodal status, proliferative marker Ki67 and Nottingham Prognostic Index in early breast cancer tumors in Saudi Population

BackgroundOncotype Dx is a 21-gene recurrence score, which is used as a diagnostic tool for the recurrence of breast cancer. It is also used to determine the benefit of chemotherapy for breast cancer in early stages. This study investigates the relationship of Oncotype Dx with pathological prognostic markers of protein Ki 67, Nottingham Prognostic Index (NPI) and tumor grade. MethodsData for early breast cancer patients treated at our tertiary care center was collected for statistical analysis. Data for patients from 2014 to 2018 was recorded for patient's age, ER/PR status, Ki 67, nodal status, tumor grade, NPI along with Oncotype Dx score. Metric measurements were described as mean ± SD and the non-metric data was represented by frequency (%). Chi-square or Fisher's exact tests as well as logistic regression was applied to assess the associations at 95% CI. ResultsAmong 156 breast cancer patients, the mean age was 55.7 ± 9.4 years. The tumors were classified into Grade-I (12.8%), Grade-II (67.3%) and Grade-III (19.9%). Ki67 score was 12.8 ± 12.0 and NPI score was 3.7 ± 0.8. The mean Oncotype Dx score was 17.0 ± 9.1; it was 14.1 ± 6.8 for Grade-I tumors; 15.7 ± 7.5 for grade -II tumors; and 23.2 ± 12.3 for grade-III tumors [Mean Oncotype Dx score across Tumor grades was compared by ANOVA (η = 0.121), p < 0.001]. While logistic regression analyses for the dichotomized Oncotype Dx higher score (≥25) was significantly associated with grade-III tumors odds ratio (OR) = 13.72 (95% CI: 1.62–115.89), higher Ki67 (>20) OR = 14.40, (95% CI: 1.44–143.71), average NPI score (2.41–3.40), OR = 13.60, (95% CI: 1.57–117.94) to poor NPI (>5.4). The association of Oncotype Dx with age, tumor size and nodal status was statistically not significant. ConclusionsThis study revealed that age, Ki67, tumor size and nodal status did not have a statistically significant impact on Oncotypye Dx recurrence score in the targeted patient population. There was a significant correlation of low grade node negative patients with Oncotype Dx while high grade node negative patients had poor correlations with Oncotype Dx. The use of Oncotype Dx has shown to be less cost-effective and has no noticeable association with improved life expectancy in the targeted patient population (i.e., hormone positive, node negative cases) in comparison with current clinical practices in Saudi Arabia and it is less likely to be cost-effective in this group of patients.

The Implementation of Nonlinear Principal Component Analysis to Acquire the Demography of Latent Variable Data (A Study Case on Brawijaya University Students)

Nonlinear principal component analysis is used for data that has a mixed scale. This study uses a formative measurement model by combining metric and nonmetric data scales. The variable used in this study is the demographic variable. This study aims to obtain the principal component of the latent demographic variable and to identify the strongest indicators of demographic formers with mixed scales using samples of students of Brawijaya University based on predetermined indicators. The data used in this study are primary data with research instruments in the form of questionnaires distributed to research respondents, which are active students of Brawijaya University Malang. The used method is nonlinear principal component analysis. There are nine indicators specified in this study, namely gender, regional origin, father's occupation, mother's occupation, type of place of residence, father's last education, mother's last education, parents' income per month, and students' allowance per month. The result of this study shows that the latent demographic variable with samples of a student at Brawijaya University can be obtained by calculating its component scores. The nine indicators formed in PC1 or X1 were able to store diversity or information by 19.49%, while the other 80.51% of diversity or other information was not saved in this PC. From these indicators, the strongest indicator in forming latent demographic variables with samples of a student of Brawijaya University is the origin of the region (I2) and type of residence (I5).

Using Predictive Analytics to Measure the Effectiveness of Select Direct Marketing Attributes in the Banking Sector

Data mining and predictive analytics are critical for the effective and sustainable functioning of the services economy. Banking is a very significant component of the services economy due to its socio-economic impact and its impact on the development of any country’s economy. The banking sector is also a major source and a subject of research for data scientists. This study uses select non-metric (demographics) and metric (direct marketing attributes) data from the UCI database. The study explores and predicts the relationship among age, bank balance and call duration of the marketing campaign. Marital status and education levels are included the measure their moderation effect on the proposed model.

Methods of a Multivariate Analysis of Non-Metric Data in Evaluating the Generational Perception of Social Characteristics

Abstract Research background: The search for factors influencing the evaluation of the quality of life in terms of subjective and objective socio-economic aspects was the background of the study. The search for perfect multivariate statistical methods in the describing of the assessments made by respondents in variable groups, as well as the categories was carried out. Purpose: The aim of the study was to recognize the natural areas of transferring subjective satisfaction with the level of social factors in the three groups describing: household, country of residence, and the EU. The determined natural relations between the factors were then compared with the established sets of those factors. The characteristics of behaviour were compared in three generations of the EU. Research methodology: The Standard Eurobarometer, autumn 2018, provided data describing adults from the generations Y, X, and BB. In the analysis a factor analysis and correspondence analysis were used. Results: The effect of the used methods is a multidirectional image of the evaluations made by the EU Generations Y, X and BB in the areas of an individual’s functioning: direct (the household), close (the country of residence), and further (Europe and the EU). Novelty: The conducted analysis indicates the need to use diverse methods in order that the assumed research objectives are thoroughly realized. The article indicates the possibility of modifying the approach in using the Burt matrix in connection with concatenated contingency tables.

The Last Glacial Maximum Microblades from Kashiwadai 1 in Hokkaido, Japan

ABSTRACT Although microliths are regarded as small standardized tools for complex composite technology, it is still not fully understood whether this schematic understanding developed in Old World prehistory can apply to the Late Pleistocene microblades in northeastern Asia. Here, referring to the definition of the Old World microliths, we explore the morphometric traits of the Late Pleistocene microblades in northeast Asia through an examination of the laminar blank production technology from the Last Glacial Maximum (LGM) microblade assemblage recovered from the Kashiwadai 1 site in Hokkaido, northern Japan. Metric and nonmetric data obtained from numerous laminar blanks reveal that microblades are comparable to bladelets without backing, as defined in the Old World records. The core reduction sequence reconstructed from the refitted specimen reveals that microblades are produced from blade core gradually reduced by careful core preparations, best labeled as the integrated laminar technology conceptually related to post-LGM bifacial microblade core technologies.

High-dimensional rank-based inference

ABSTRACTExisting high-dimensional inferential methods for comparing multiple groups test hypotheses are formulated in terms of mean vectors or location parameters. These methods are applicable mainly for metric data. Furthermore, the mean-based methods assume that moments exist and the nonparametric (location-based) ones assume elliptical-contoured distributions for the populations. In this paper, a fully nonparametric (rank-based) method is proposed. The method is applicable for metric as well as non-metric data and, hence, is applicable for ordered categorical as well as skewed and heavy tailed data. To develop the theory, we prove a novel result for studying asymptotic behaviour of quadratic forms in ranks. Simulation study shows that the developed rank-based method performs comparably well with mean-based methods when the assumptions of those methods are satisfied. However, it has significantly superior power for heavy tailed distributions with the possibility of outliers. The rank method is applied to an EEG data with the objective of examining associations between alcohol use and change in brain function.

Neighbor-rank densities for non-metric data

In this work we propose rank densities, a novel density measure for non-metric data. Unlike typical measures employed in density clustering algorithms, rank densities are defined via ranks of patterns in k-nearest neighbor lists. Therefore they depend on the structure of the k-nearest neighbor graph, rather than exact values of the similarity measure. This property makes them robust to noise and easier to use with complicated similarity measures. We propose a simple iterative algorithm to estimate rank densities and demonstrate that it converges to a solution that does not depend on the initial configuration or the optimization step. Finally, we demonstrate an example application of rank densities to a real-world non-metric dataset.