Empirical Process Research Articles

A Flexible Risk-Based Security Evaluation Methodology for Information Communication Technology System Certification

As Information and Communication Technology (ICT) systems become increasingly complex, the need for adaptable and efficient security certification frameworks grows. This paper introduces a flexible security evaluation methodology designed to serve as the foundation for cybersecurity certification across diverse ICT systems. The proposed methodology integrates risk assessment and test-based evaluation, offering a scalable approach that adapts to different tools and processes, addressing the limitations of existing rigid certification schemes. The certification approach expands on ETSI’s Risk-Based Security Assessment and Testing methods, based on ISO 31000 and ISO 29119, and it integrates widely recognized standards such as MUD. This ensures an objective, empirical evaluation process that enables partial automation and simplifies recertification. As a proof of concept, we validate the methodology in two real use cases, an ICT gateway for smart grids and an AI-powered investments platform, demonstrating its flexibility and applicability to real-world contexts while addressing the challenges of modern ICT ecosystems.

What is transformative in participatory approaches to territorial agroecological transitions? A systematization of five case studies in Spain

ABSTRACT Participatory processes of agroecological transitions at territorial scales are becoming a widespread practice. However, systematic research based on empirical processes remains scarce. In this paper, we systematize the experiences of five cases of co-design for agroecological transitions in Spain, in different territorial contexts and scales, applying the framework of Local Agroecological Dynamization. The systematization has involved professional facilitators of each project and is based on the primary and secondary data they provided. The systematization describes a sequence of milestones to walk through to implement transformative, participatory processes of transitions and suggests some principles for the design of such processes. The paper highlights two elements that define the transformative character of the cases: the activation of social creativity based on the material and relational features of the territory, and the strengthening of local socio-economic actors in the framework of a plural social subject to promote the transition. More empirical, action-oriented research is needed, in different territorial contexts and long-term processes, to deepen the understanding of such issues.

Nearest neighbor empirical processes

Nearest neighbor empirical processes

Understanding State Dysfunctionality: The Role of Political Elites in South Sudanese State-crafting and Failure

State crafting, dysfunctionality and failure is an interesting and an emerging area in political studies as well as international affairs. This area has been remotely examined by both African and Western scholars. The paper comprehensively examined state dysfunctionality in the context of state failure of South Sudan. The paper conceptualized state dysfunctionality as inability of the state to perform its functions of service delivery of public goods and particularly, security to its own citizens. While the paper surveyed the role of political elites in understanding state-crafting and failure of South Sudan, empirically, its argues that South Sudanese political elites, particularly, from Sudan Peoples’ Liberation Movement (SPLM) and Sudan People’s Liberation Army (SPLA) known today as South Sudanese People Defense Forces (SSPDF) have contributed to South Sudanese state failure than crafting. This is demonstrated through elites struggle over power, secretive ethnic politics and rewarding rebellions, corruption and resources usurp and protracted conflicts. The paper deployed primary and secondary sources in tapping the understanding of South Sudanese political elites in state-crafting and failure. It combines case study and process tracing methods to contextualize and validate causal chains and empirical casual processes. The study used a sample size of 200 respondents with persuasive and cluster sampling in understanding state dysfunctionality, the role political elites in South Sudanese state-crafting and failure. The findings indicated that political elites from Government of South Sudan and particularly, the party with majority seats in the government, SPLM and military wing, SPLA aka SSPDF have led to South Sudanese state failure. The tribal outfits such as the Jieng Council of Elders (JCE) have had a big hand in South Sudanese state failure. Finally, the paper draws conclusions that reversing South Sudanese state failure requires the political elites, the SPLM to eschew zero-sum power struggle, rent seeking rebellions, secretive ethnic politics, conflicts and corruption. This demands adherence to institutionalism and visionary leadership. The paper recommends further research to SPLM and SPLA elites to reverse state failure and rescue South Sudan from collapse.

Properties of the vertex of a convex hull generated by a Poisson point process inside a parabola

A convex hull generated by the implementation of a Poisson point process inside a parabola is considered in the article. At that, the measure of intensity of the Poisson law is related to regularly varying functions near the boundary of the support. It is proven that the domain bounded by the perimeters of the convex hull and the boundary of the support - a parabola, can be represented as a sum of independent identically distributed random variables. Moreover, this value does not depend on the vertices of the convex hull itself. It is worth noting that having approximated the binomial point process by a Poisson one, P.Groeneboom [6], A.J.Cabo and P.Groeneboom [3], I.Hueter [9], T.Hsing [8] and others, using the martingale properties of stationary vertex processes, proved various options of the central limit theorem for functionals of a random convex hull in the case when the original distribution is uniformly concentrated in a convex polygon or ellipse. In this paper, the exact distribution and conditional distribution of vertex processes are found when the convex hull is generated by a inhomogeneous Poisson point process inside a parabola. In some special cases, it is shown that the area between the perimeter of the convex hull and the support of the distribution is expressed by the sum of independent random variables.

Deep Regression for Repeated Measurements

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected deep neural network (DNN) estimators with flexible shapes. A novel theoretical framework allowing arbitrary sampling frequency is established by adopting empirical process techniques to tackle clustered dependence. We then consider the DNN estimators for Hölder target function and illustrate a key phenomenon, the phase transition in the convergence rate, inherent to repeated measurements and its connection to the curse of dimensionality. Furthermore, we study several examples with low intrinsic dimensions, including the hierarchical composition model, low-dimensional support set and anisotropic Hölder smoothness. We also obtain new approximation results and matching lower bounds to demonstrate the adaptivity of the DNN estimators for circumventing the curse of dimensionality. Simulations and real data examples are provided to support our theoretical findings and practical implications.

Estimation and specification test for diffusion models with stochastic volatility

Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical process of the residuals built with an adapted Kalman Filter estimation. The test statistics are constructed using a continuous functional (Kolmogorov–Smirnov and Crámer–von Mises) over the empirical processes. Both, the different estimation procedures (including other alternatives as for example methods based on Markov Chain Monte Carlo or Particle filters) and the new proposed tests are compared in different simulation studies. The tests are calibrated with a specific bootstrap method using the estimation of a discrete version of the diffusion model with stochastic volatility. Finally, an application of the procedures to real data is provided.

Compound Poisson particle approximation for McKean–Vlasov SDEs

Abstract We present a comprehensive discretization scheme for linear and nonlinear stochastic differential equations (SDEs) driven by either Brownian motions or $\alpha $-stable processes. Our approach utilizes compound Poisson particle approximations, allowing for simultaneous discretization of both the time and space variables in McKean–Vlasov SDEs. Notably, the approximation processes can be represented as a Markov chain with values on a lattice. Importantly, we demonstrate the propagation of chaos under relatively mild assumptions on the coefficients, including those with polynomial growth. This result establishes the convergence of the particle approximations towards the true solutions of the McKean–Vlasov SDEs. By only imposing moment conditions on the intensity measure of compound Poisson processes our approximation exhibits universality. In the case of ordinary differential equations (ODEs) we investigate scenarios where the drift term satisfies the one-sided Lipschitz assumption. We prove the optimal convergence rate for Filippov solutions in this setting. Additionally, we establish a functional central limit theorem for the approximation of ODEs and show the convergence of invariant measures for linear SDEs. As a practical application we construct a compound Poisson approximation for two-dimensional Navier–Stokes equations on the torus and demonstrate the optimal convergence rate.

Two-Sample Distribution Tests in High Dimensions via Max-Sliced Wasserstein Distance and Bootstrapping

Summary Two-sample hypothesis testing is a fundamental statistical problem for inference about two populations. In this paper, we construct a novel test statistic to detect high-dimensional distributional differences based on the max-sliced Wasserstein distance to mitigate the curse of dimensionality. By exploiting an intriguing link between the distance and suprema of empirical processes, we develop an effective bootstrapping procedure to approximate the null distribution of the test statistic. One distinctive feature of the proposed test is the ability to construct simultaneous confidence intervals for the max-sliced Wasserstein distances of projected distributions of interest. This enables not only the detection of global distributional differences but also the identification of significantly different marginal distributions between two populations, without the need for additional tests. We establish the convergence of Gaussian and bootstrap approximations of the proposed test, based on which we show that the test is asymptotically valid and powerful as long as the considered max-sliced Wasserstein distance is adequately large. The merits of our approach are illustrated via simulated and real data examples.

K-Nearest Neighbour Estimation of the Conditional Set-Indexed Empirical Process for Functional Data: Asymptotic Properties

k-Nearest Neighbour Estimation of the Conditional Set-Indexed Empirical Process for Functional Data: Asymptotic Properties

Item Classification by Difficulty Using Functional Principal Component Clustering and Neural Networks.

Maintaining consistent item difficulty across test forms is crucial for accurately and fairly classifying examinees into pass or fail categories. This article presents a practical procedure for classifying items based on difficulty levels using functional data analysis (FDA). Methodologically, we clustered item characteristic curves (ICCs) into difficulty groups by analyzing their functional principal components (FPCs) and then employed a neural network to predict difficulty for ICCs. Given the degree of similarity between many ICCs, categorizing items by difficulty can be challenging. The strength of this method lies in its ability to provide an empirical and consistent process for item classification, as opposed to relying solely on visual inspection. The findings reveal that most discrepancies between visual classification and FDA results differed by only one adjacent difficulty level. Approximately 67% of these discrepancies involved items in the medium to hard range being categorized into higher difficulty levels by FDA, while the remaining third involved very easy to easy items being classified into lower levels. The neural network, trained on these data, achieved an accuracy of 79.6%, with misclassifications also differing by only one adjacent difficulty level compared to FDA clustering. The method demonstrates an efficient and practical procedure for classifying test items, especially beneficial in testing programs where smaller volumes of examinees tested at various times throughout the year.

Functional Central Limit Theorems for epidemic models with varying infectivity and waning immunity

We study an individual-based stochastic epidemic model in which infected individuals gradually become susceptible again following each infection (generalized SIS model). The epidemic dynamics is described by the average infectivity and susceptibility processes in the population together with the numbers of infected and susceptible/uninfected individuals. In R. Forien et al., Stochastic epidemic models with varying infectivity and susceptibility. arXiv preprint arXiv:2210.04667 (2022), a functional law of large numbers (FLLN) is proved as the population size goes to infinity, and asymptotic endemic behaviors are also studied. In this paper, we prove a functional central limit theorem (FCLT) for the stochastic fluctuations of the epidemic dynamics around the FLLN limit. The FCLT limit for the aggregate infectivity and susceptibility processes is given by a system of stochastic non-linear integral equation driven by a two-dimensional Gaussian process.

Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation

Asymptotic behavior of the empirical checkerboard copula process for binary data: An educational presentation

Sieve Maximum Likelihood Estimation of Partially Linear Transformation Models With Interval-Censored Data.

Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval-censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow-up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval-censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and -splines, respectively. We develop an easy-to-implement expectation-maximization algorithm coupled with three-stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness.

Student collaboration skills post-implementation of the WE-ARe model

Collaboration skills are fundamental to helping students face challenges in education and work. However, there is limited research on students’ collaboration skills, particularly using a specific model. This present study aims to analyze the influence of the Warm-up, Exploring, Argumentation, Resume (WE-ARe) model on students' collaboration skills. We employed a quasi-experimental design with a Pre-test and Post-test Group Design. The sample was Islamic High School of Eleventh Grade Natural Science Program-2, totalling 28 people. The data was obtained through questionnaires, observation, and interview questions with instruments validated by experts and empirical processes. The t-test results show that the WE-ARe learning model significantly influences students’ collaboration skills with a t-count of 47.753 (sig. 0.000). This finding indicates that the research hypothesis concerning differences in students' pre-test and post-test collaboration skills in the WE-ARe learning model was accepted, signifying that the WE-ARe learning model improves students’ collaboration skills. It can be concluded that the WE-ARe model influences students' collaboration skills. This finding implies that the WE-ARe model can be an alternative innovative model in accommodating students’ collaboration skills in learning.

Understanding State Formation: The Role of Political Parties in South Sudanese State-crafting and Failure

State crafting, failure and, collapse is an interesting area of social science research, which has been remotely examined by comparative political scientists. The paper comprehensively examines the crafting and failure of South Sudanese state. It conceptualizes state, state-crafting, state failure and collapse. It surveys the role of political parties in understanding state-crafting and failure in South Sudan. Empirically, the paper argues that South Sudanese political parties particularly, Sudan People’ Liberation Movement (SPLM) have contributed in South Sudanese failure than crafting and prosperity. This is demonstrated through ethnicization of politics and politicization of ethnicity and through ethnic divisions. Using empirical literature, the paper discusses state crafting, failure and dissects the role of political parties in which SPLM has a big hand in the state failure of South Sudan. In its methodology, the paper deploys primary and secondary sources in tapping the understanding of the role of South Sudanese political parties in state-crafting and failure. Primary data include the use of questionnaires and interviews in comprehending state formation and in particular, the role played by South Sudanese political parties in nascent state-crafting and failure. Secondary sources include the use of literature review in understanding political parties and their role in South Sudanese state failure. The study uses a sample size of 200 respondents with sample types of persuasives and cluster sampling combined. The study also combines case study and process tracing methods to contextualize and validate causal chains and empirical casual processes of South Sudan state formation and role of political parties in state-crafting and failure. The results of the study indicate that SPLM as a main ruling party has a huge contribution in South Sudanese state failure. While other 28 registered political parties are ethnic-based given that because they don’t have national programmes across South Sudan, their contributed to South Sudanese state failure cannot be equated with SPLM. These 28 parties have their presence in the bomas, payams and counties only and have endeavored to promote ethnic divisions and violence in South Sudan. Finally, the paper draws conclusions on the need for civic role of political parties in state-crafting and democratization of South Sudan. The paper recommends future research on the role of SPLM party in reversing state failure and rescuing South Sudan from collapse.

Goodness-of-Fit Testing for a Regression Model With a Doubly Truncated Response.

In survival analysis and epidemiology, among other fields, interval sampling is often employed. With interval sampling, the individuals undergoing the event of interest within a calendar time interval are recruited. This results in doubly truncated event times. Double truncation, which may appear with other sampling designs too, induces a selection bias, so ordinary statistical methods are generally inconsistent. In this paper, we introduce goodness-of-fit procedures for a regression model when the response variable is doubly truncated. With this purpose, a marked empirical process based on weighted residuals is constructed and its weak convergence is established. Kolmogorov-Smirnov- and Cramér-von Mises-type tests are consequently derived from such core process, and a bootstrap approximation for their practical implementation is given. The performance of the proposed tests is investigated through simulations. An application to model selection for AIDS incubation time as depending on age at infection isprovided.

Natural and Artificial Intelligence Interactions in Digital Networking: A Multilayer Network Model for Economic Value Creation

This study investigates the integration of natural intelligence (NI) and artificial intelligence (AI) within traditional firms linked through a multilayer network framework. The research explores this central question: How can the integration of NI and AI, facilitated by copula nodes, drive economic value creation in digitized firms? The paper combines theoretical and empirical results of the observed increments in cost-benefit marginality linked with AI adoption by checking out testing in various domains such as manufacturing, retailing, finance, etc. The performance of the model shows enhanced efficiency and decision-making, as well as savings in costs. Copula nodes that connect multilayer networks blend NI with AI, boosting overall value. Unlike existing studies, this framework operationalizes copula nodes to capture real-time dependencies between human-driven and AI-driven processes, offering a comprehensive view of economic value creation across digitized firms. A methodology section outlines the empirical validation process conducted across multiple industries (manufacturing, retail, and finance), providing key insights into efficiency, decision-making, and cost optimization. The practical implications offer a strategic pathway for firms to enhance profitability and competitiveness in the digital age. The results underscore the importance of strategically integrating AI with human intelligence to maximize economic outcomes. Received: 18 August 2024 | Revised: 22 October 2024 | Accepted: 10 November 2024 Conflicts of Interest The author declares that he has no conflicts of interest to this work. Data Availability Statement Data sharing is not applicable to this article as no new data were created or analyzed in this study. Author Contribution Statement Roberto Moro Visconti: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data Curation, Writing - Original Draft, Writing -Review & Editing, Visualization, Supervision, Project administration, Funding acquisition.

A hybrid approach for modelling safety hazards in China subways: multi-stakeholders’ perspective

PurposeUnlike previous research that primarily utilized structural equation modelling (SEM) to evaluate safety hazards in subway projects, this research aims to utilize a hybrid approach to investigate and scrutinize the key indicators of safety hazards leading to accidents, thereby hindering the progress of subway projects in China, taking into cognizance the multiple stakeholder’s perspective.Design/methodology/approachBy administering a survey questionnaire to 373 highly involved stakeholders in subway projects spanning Changsha, Beijing and Qingdao, China, our approach incorporated a four-staged composite amalgamation of exploratory factor analysis (EFA), confirmatory factor analysis (CFA), covariance-based structural equation modelling (CB-SEM) and artificial neural network (ANN) to develop an optimized model that determines the causal relationships and interactions among safety hazards in subway construction projects.FindingsThe optimized model delineated the influence of individual safety hazards on subway projects. The feasibility and applicability of the model developed was demonstrated on an actual subway project under construction in Changsha city. The outcomes revealed that the progress of subway projects is significantly influenced by risks associated with project management, environmental factors, subterranean conditions and technical hazards. In contrast, risks related to construction and human factors did not exhibit a significant impact on subway construction progress.Research limitations/implicationsWhile our study provides valuable insights, it is important to acknowledge the limitation of relying on theoretical approaches without empirical validation from experiments or the field. In future research, we plan to address this limitation by assessing the SEM using empirical data. This will involve a comprehensive comparison of outcomes derived from CB-SEM with those obtained through SEM-ANN methods. Such an empirical validation process is crucial for enhancing the overall efficiency and robustness of the proposed methodologies.Originality/valueThe established hybrid model revealed complex non-linear connections among indicators in the intricate project, enabling the recognition of primary hazards and offering direction to improve management of safety in the construction of subways.

Synthesis Pathway Oriented Heterogeneous Stacking Mode of Homogeneous Two-Dimensional Hydrazone-Linked COFs

The study of isomerism phenomena in covalent organic frameworks (COFs), such as dimensional isomerism, interpenetration isomerism, and stacking isomerism, along with their influence on the properties of COFs, has become an intriguing research avenue in recent years. Nevertheless, the current techniques for synthesizing COF isomers predominantly rely on extensive trial and error, lacking efficient, target-driven synthetic methodologies. The development of synthetic protocols capable of selectively enhancing the crystallization of one COF isomer over another continues to pose a significant challenge, remaining an empirical process at present. In this work, through subtly designing with the same structure and different stacking modes, we elucidate how altering the sequence of hydroxyl site modifications on the monomer impacts dissolution, polymerization, and assembly processes during COF synthesis, thereby influencing the stacking modes of two kinds of hydrazine-linked COFs with reversed AA stacking and AA stacking structures. The quasi-in-situ PXRD analysis during methanol volatilization and the N2 adsorption experiments revealed that the crystallinity and stability of the COFs prepared by the pre- and post-modified method are significantly different. These structural differences are further reflected in applications such as photocatalytic reduction of uranium and iodine adsorption. This work sheds light on the crucial role of non-covalent interactions in influencing and regulating the stability-crystallinity-functionality of COFs, offering valuable insights for future investigations.