Article
Mathematics, Applied
Thimo M. Kasper, Nicolas Dietrich, Wolfgang Trutschnig
Summary: Motivated by a recently established result, this contribution studies the convergence properties of Archimedean copulas and their conditional distribution functions. Several properties equivalent to pointwise convergence are established and alternative proofs for well-known formulas are provided. The application of Williamson measures allows for simplified expressions and characterization of pointwise convergence. The study also explores the density of absolutely continuous and singular copulas and highlights the potential singularity behavior of Archimedean copulas in conditional distribution functions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Engineering, Civil
Shahid Latif, Slobodan P. Simonovic
Summary: The joint probability modelling of storm surges and rainfall events in low-lying coastal areas is crucial for assessing compound flood risk. This study proposes a nonparametric approach using the Bernstein copula estimator and Beta kernel copula density. The research shows that neglecting the compound effect of storm surge and rainfall in coastal flood risk assessment may lead to underestimated failure probability statistics.
WATER RESOURCES MANAGEMENT
(2022)
Article
Mathematics, Applied
Qingsong Shan, Qianning Liu
Summary: This paper introduces a new method for measuring functional dependence called MFD, which uses a beta kernel estimator. The proposed estimator is shown to be highly accurate in estimation through simulated examples and analysis of real data.
Article
Statistics & Probability
Thomas Mroz, Juan Fernandez Sanchez, Sebastian Fuchs, Wolfgang Trutschnig
Summary: Motivated by the lifetimes of electronic components or financial institutions, this paper investigates the problem of maximizing the probability that a random variable X is not smaller than another random object Y, and that X and Y coincide within the class of all random variables with given continuous distribution functions. The paper introduces copulas and provides proofs for two maximization problems related to copulas. Generalizations and formulas for non-monotonic transformations are derived, and an estimator for the maximum probability is presented. The importance of the tackled questions is demonstrated through applications to relative effects.
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
(2023)
Article
Physics, Multidisciplinary
M. El-Morshedy, Fahad Sameer Alshammari, Yasser S. Hamed, Mohammed S. Eliwa, Haitham M. Yousof
Summary: In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Several new bivariate G families based on different copula theorems are presented. The maximum likelihood method is used to estimate model parameters, with a graphical simulation to assess the performance of the estimators. Two real-life data applications highlight the significance of the new family.
Article
Computer Science, Information Systems
Aref Majdara, Saeid Nooshabadi
Summary: This paper presents an efficient algorithm for density estimation in high-dimensional data analysis, along with the corresponding data structures and algorithm. The algorithm is based on Bayesian inference and utilizes copula transformation to optimize the computational efficiency of density estimation. Furthermore, the algorithm is suitable for parallel processing.
Article
Statistics & Probability
Pierre Alquier, Badr-Eddine Cherief-Abdellatif, Alexis Derumigny, Jean-David Fermanian
Summary: This article discusses the robust inference problem for parametric copula models, proposes a method based on the maximum mean discrepancy principle, and derives nonasymptotic oracle inequalities and asymptotic normality. The method does not require any assumption on the copula family and can handle outliers and misspecification. Moreover, it can handle copula models for which there exists no density with respect to the Lebesgue measure on [0,1]d.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Operations Research & Management Science
Alessandro Barbiero
Summary: In many real-world applications, continuous phenomena are often modeled using continuous probability distributions. However, the observed values are actually discrete. This paper discusses two methods for deriving bivariate discrete probability distributions from continuous ones. The paper also presents examples and numerical studies to illustrate how the discretization procedures work and their impact on the original model's dependence structure. Additionally, the paper proves that some recently proposed bivariate discrete distributions can be considered as discrete counterparts of well-known continuous models. The practical implementation and inferential aspects are also presented.
ANNALS OF OPERATIONS RESEARCH
(2022)
Article
Automation & Control Systems
Gianluigi Pillonetto, Akram Yazdani
Summary: This paper addresses the challenging problem of identifying dynamic networks and proposes a novel Bayesian approach that accurately reconstructs the network dynamics without prior knowledge of the topology.
Article
Water Resources
David A. Benson, Diogo Bolster, Stephen Pankavich, Michael J. Schmidt
Summary: Traditional interpolation techniques for particle tracking involve binning and convolutional formulas using pre-determined kernels. Each particle in the cloud is a sample from the Green's function, and the kernel for interpolation should replicate the cloud itself. An iterative method is proposed to discern the form of the kernel during the process of interpolating the Green's function.
ADVANCES IN WATER RESOURCES
(2021)
Article
Mathematics
Catalina Bolance, Carlos Alberto Acuna
Summary: This paper investigates copulas with marginal distributions Uniform(0,1), improving the kernel estimator using a Beta quantile transformation. Simulation studies show that this method enhances copula estimators compared to alternative kernel estimators.
Article
Economics
Lu Yang
Summary: Multivariate claim data are essential for insurers to ensure solvency and profitability. Copula models are commonly used to quantify the dependencies among such data, but existing methods do not work for mixed data. This article fills this gap by developing a nonparametric copula estimator for mixed data and demonstrates its performance.
JOURNAL OF BUSINESS & ECONOMIC STATISTICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ibrahim Alkhairy, M. Nagy, Abdisalam Hassan Muse, Eslam Hussam
Summary: This research introduces a new family of distributions based on the inverse trigonometric function Arctan-X, with a focus on the special case of the Arctan-Weibull distribution. Maximum likelihood estimation is used to estimate the parameters of the Arctan-Weibull distribution, and a rigorous Monte Carlo simulation analysis is conducted to assess the efficiency of the estimators. The Arctan-Weibull model is compared to several well-known competitors, such as Weibull, Kappa, Burr-XII, and beta-Weibull, using precise tests to determine its superiority in modeling complex data sets.
Article
Automation & Control Systems
Jia Guo, Sai Tej Paruchuri, Andrew J. Kurdila
Summary: An adaptive nonparametric method is proposed in this article to estimate unknown scalar-valued functions in systems governed by ordinary differential equations (ODEs). The convergence analysis is facilitated by introducing a novel condition of partial persistent excitation (partial PE), and the effectiveness of the research results is illustrated through numerical simulations.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Statistics & Probability
Oskar Laverny, Esterina Masiello, Veronique Maume-Deschamps, Didier Rulliere
Summary: The CORT estimator is a flexible and consistent copula estimator that recursively constructs a grid from data, ensuring dependence and guaranteeing uniformity of margins.
JOURNAL OF MULTIVARIATE ANALYSIS
(2021)
Article
Computer Science, Interdisciplinary Applications
A. Meilan-Vila, M. Francisco-Fernandez, R. M. Crujeiras
Summary: This work proposes testing procedures for assessing a parametric regression model with a circular response and an R-d-valued covariate. The test statistics are based on comparing a parametric circular regression estimator and a nonparametric one using circular distance. Two bootstrap procedures for calibrating the tests in practice are also presented. The finite sample performance of the tests in different scenarios is analyzed by simulations and illustrated with real data examples.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2022)
Article
Statistics & Probability
Paula Saavedra-Nieves, Rosa M. Crujeiras
Summary: In this study, directional highest density regions (HDRs) are formally defined and plug-in estimators based on kernel smoothing are proposed. A new bootstrap bandwidth selector is provided for HDRs estimation, showing good performance in simulations and real data sets related to animal orientation and seismology.
ADVANCES IN DATA ANALYSIS AND CLASSIFICATION
(2022)
Article
Biodiversity Conservation
Ramiro Martin-Devasa, Sara Martinez-Santalla, Carola Gomez-Rodriguez, Rosa M. Crujeiras, Andres Baselga
Summary: This study aimed to assess the dependence between the form of the decrease in biological similarity with distance (distance-decay) and species range size, and introduced the use of a sigmoidal model, the Gompertz function, for fitting distance-decay models. The results showed that the functional form of distance-decay patterns depends on species range size, and the Gompertz function accommodates different frequency distributions of species range size.
DIVERSITY AND DISTRIBUTIONS
(2022)
Article
Ecology
Sara Martinez-Santalla, Ramiro Martin-Devasa, Carola Gomez-Rodriguez, Rosa M. Crujeiras, Andres Baselga
Summary: Modeling community similarity decay with spatial distance is important for studying community variation. A new nonlinear significance test combining R-2 statistic with permutations was proposed, showing good performance for nonlinear relationships. This test should be favored over linear Mantel test for assessing distance-decay patterns.
JOURNAL OF BIOGEOGRAPHY
(2022)
Article
Mathematical & Computational Biology
Wenceslao Gonzalez-Manteiga, Maria Dolores Martinez-Miranda, Ingrid Van Keilegom
Summary: This paper discusses the testing of covariate effects in a Cox proportional hazards model with random effects. It considers the clustered and incomplete nature of the response data due to right censoring. The estimation of the model is done using the full marginal likelihood under both parametric and nonparametric effects. The proposed testing procedure is evaluated through simulations and applied to real data from biomedical research and veterinary medicine.
BIOMETRICAL JOURNAL
(2023)
Article
Computer Science, Interdisciplinary Applications
Alberto Fernandez-de-Marcos, Eduardo Garcia-Portugues
Summary: Obtaining exact null distributions for goodness-of-fit test statistics is difficult, so practitioners often rely on asymptotic null distributions or Monte Carlo methods. This study presents improved methods for stabilizing the exact critical values and obtaining exact p-values for various classic and novel test statistics used for goodness-of-fit testing. These methods have been applied and shown to be effective in analyzing small-to-moderate sequentially-measured samples in astronomy.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Statistics & Probability
Pavlos Zoubouloglou, Eduardo Garcia-Portugues, J. S. Marron
Summary: This article introduces Scaled Torus Principal Component Analysis (ST-PCA), a novel approach for dimensionality reduction with toroidal data. ST-PCA finds a data-driven map from a torus to a sphere of the same dimension and radius, enabling meaningful dimensionality reduction.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2023)
Article
Statistics & Probability
Eduardo Garcia-Portugues, Paula Navarro-Esteban, Juan A. Cuesta-Albertos
Summary: We introduce a projection-based class of uniformity tests on the hypersphere, which integrates statistics along all possible directions. The class provides simple expressions for test statistics on the circle and sphere, and relatively tractable forms for higher dimensions. The proposed class contains and is contained in variants of the Sobolev class of uniformity tests. It allows the derivation of new tests that extend existing circular-only tests and introduces a new Anderson-Darling-like test for directional data.
Article
Computer Science, Artificial Intelligence
Ameed Almomani, Paula Saavedra, Pablo Barreiro, Roi Duran, Rosa Crujeiras, Maria Loureiro, Eduardo Sanchez
Summary: Choice models (CM) are proposed to overcome the limitations of current algorithms in tourism recommender systems (TRS), providing accurate preferences and interpretable coefficients. Results show that CM outperforms baseline algorithms when the choice set is limited. CM may provide an optimal trade-off between theoretical soundness, interpretability, and performance in TRS.
Article
Statistics & Probability
Maria Alonso-pena, Rosa M. Crujeiras
Summary: In this paper, a nonparametric method is proposed to estimate the conditional local modes of animal escape directions. The method is tested through simulation experiments and applied to model the escape behavior of larval zebrafish. The approach presented in this paper can have broader applications in animal behavior and other fields.
ANNALS OF APPLIED STATISTICS
(2023)
Article
Biology
Zihao Wu, Carolina Euan, Rosa M. Crujeiras, Ying Sun
Summary: The directional wave spectrum (DWS) is a useful tool for marine studies and the design of maritime structures. This paper addresses the challenge of accounting for the circular nature of direction in the statistical estimation of DWS. It proposes using circular regression to smooth the observations and improve clustering algorithms for DWS analysis. Simulation studies and real data analysis demonstrate the effectiveness of the proposed circular smoother.
JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS
(2023)
Article
Statistics & Probability
Andrea Meilan-Vila, Rosa M. Crujeiras, Mario Francisco-Fernandez
Summary: Changes in temperature patterns are the most direct indicators of global warming and climate change, especially on a local scale. This study focuses on a regression model that relates temperature curves to calendar days, and evaluates temperature changes through prediction and observation comparisons. The model considers a nonparametric Nadaraya-Watson-type estimator for functional covariate and circular response, and its asymptotic bias, variance, and distribution are derived. The finite sample performance is evaluated through simulation studies and real-data analysis of temperature curves.
STATISTICAL PAPERS
(2023)
Article
Mathematics, Applied
Ralph G. Andrzejak, Anais Espinoso, Eduardo Garcia-Portugues, Arthur Pewsey, Jacopo Epifanio, Marc G. Leguia, Kaspar Schindler
Summary: The article introduces how to quantify the concentration of unimodal circular data around the mean direction using the mean resultant length, and proposes a re-normalized version as an improvement. The relevance and effectiveness of the proposed method are illustrated through examples.
Article
Statistics & Probability
Alberto Fernandez-de-Marcos, Eduardo Garcia-Portugues
Summary: This study proposes two new omnibus tests for data on the hypersphere, which exploit closed-form expressions for orthogonal polynomials and feature tuning parameters related to a smooth maximum function and the Poisson kernel. The study obtains exact moments and null asymptotic distributions of the test statistics, and considers approximate oracle tuning parameters that maximize the power of the tests. Numerical experiments and simulations demonstrate the effectiveness and accuracy of the proposed tests, which are also applied to the study of nursing times of wild polar bears.
Article
Computer Science, Interdisciplinary Applications
Paula Saavedra-Nieves, Rosa M. Crujeiras
Summary: HDiR is a package for R that computes directional highest density regions and density level sets. It also supports nonparametric plug-in methods for incomplete density and level set computation for general functions.
