Nonparametric Estimation of Multivariate Extreme Value Copulas with Known and Unknown Marginal Distributions

The purpose of this paper is estimating the dependence function of multivariate extreme values copulas. Different nonparametric estimators are developed in the literature assuming that marginal distributions are known. However, this assumption is unrealistic in practice. To overcome the drawbacks of these estimators, we substituted the extreme value marginal distribution by the empirical distribution function. Monte Carlo experiments are carried out to compare the performance of the Pickands, Deheuvels, Hall-Tajvidi, Zhang and Gudendorf-Segers estimators. Empirical results showed that the empirical distribution function improved the estimators’ performance for different sample sizes.

Detecting Financial Statement Fraud with Interpretable Machine Learning

In this study, we explored a stable and explainable model in the detection of financial fraud. To effectively handle imbalanced datasets, we selected the Smote oversampling algorithm with the highest AUC value and compared it with Borderline Smote and ADASYN algorithms. Using the MCB method, we found that the Adaptive Lasso algorithm had higher stability than SCAD, MCP, Stepwise, and SQRT Lasso algorithms. Moreover, the AUC value was improved by WoE encoding and IV value testing of the features. Finally, we ranked the fraud factors based on the importance of the features, and the partial dependence function was used to make the model interpretable. By comparing the AUC and KS values, the integrated models XGBoost, LightGBM, and RF showed better ability to identify financial fraud compared with traditional models such as SVM and LR.

Development of a prognostic prediction model to estimate the risk of multiple chronic diseases

IntroductionThe ability to estimate risk of multimorbidity will provide valuable information to patients and primary care practitioners in their preventative efforts. Current methods for prognostic prediction modelling are insufficient for the estimation of risk for multiple outcomes, as they do not properly capture the dependence that exists between outcomes. ObjectivesWe developed a multivariate prognostic prediction model for the 5-year risk of diabetes, hypertension, and osteoarthritis that quantifies and accounts for the dependence between each disease using a copula-based model. MethodsWe used data from the Canadian Primary Care Sentinel Surveillance Network (CPCSSN) from 2009 onwards, a collection of electronic medical records submitted by participating primary care practitioners across Canada. We identified patients 18 years and older without all three outcome diseases and observed any incident diabetes, osteoarthritis, or hypertension within 5-years, resulting in a large retrospective cohort for model development and internal validation (n=425228). First, we quantified the dependence between outcomes using unadjusted and adjusted ϕ coefficients. We then estimated a copula-based model to quantify the non-linear dependence between outcomes that can be used to derive risk estimates for each outcome, accounting for the observed dependence. Copula-based models are defined by univariate models for each outcome and a dependence function, specified by the parameter θ. Logistic regression was used for the univariate models and the Frank copula was selected as the dependence function. ResultsAll outcome pairs demonstrated statistically significant dependence that was reduced after adjusting for covariates. The copula-based model yielded statistically significant θ parameters in agreement with the adjusted and unadjusted ϕ coefficients. Our copula-based model can effectively be used to estimate trivariate probabilities. DiscussionQuantitative estimates of multimorbidity risk inform discussions between patients and their primary care practitioners around prevention in an effort to reduce the incidence of multimorbidity.

Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application

The paper investigates the Hoeffding–Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transferred to the terms of the functional decomposition, and in addition to their individual variances, or to the superset combinations of those. The domain of integration in the resulting formulae is reduced in comparison with the already known expressions. When the function under study is the stable tail dependence function of a random vector, ranking these superset indices corresponds to clustering the components of the random vector with respect to their asymptotic dependence. Their Choquet representation is the main ingredient in deriving a sharp upper bound for the quantities involved in the tail dependograph, a graph in extreme value theory that summarizes asymptotic dependence.

Global Hierarchical Models for Wind and Wave Contours: Physical Interpretations of the Dependence Functions

Applications such as the design of offshore wind turbines requires the estimation of the joint distribution of variables like wind speed, wave height and wave period. The joint distribution can then be used, for example, to define design load cases using the environmental contour method. Often the joint distribution is described using so-called global hierarchical models. In these models, one variable is taken as independent and the other variables are modelled to be conditional on this variable using particular dependence functions. In this paper, we propose to use dependence functions that offer physical interpretation. We define a novel dependence function that describes how the median of the zero-up-crossing period increases with significant wave height and a novel dependence function that describes how the median significant wave height increases with wind speed. These dependence functions allow us to reason about the physical meaning, even when we extrapolate outside the range of a given sample of environmental data. In addition, we can analyze the estimated parameters of the dependence function to speculate which kind of sea dominates at a given site. We fitted statistical models with the proposed dependence functions to six datasets and analyzed the estimated parameters. Then we calculated environmental contours based on these estimated joint distributions. The environmental contours had physically reasonable shapes, even at areas that were outside the datasets that were used to fit the underlying distributions.

Innovative Technologies and Social Responsibility of Business: Analysis of Possibilities

The mechanism of organization and prediction regarding the main indicators of innovative business on the example of disposable cookware production made from bran is offered in the article. The statistical study of the potential demand for this cookware is conducted. The three-factor linear dependence function is constructed. The relationship between the change in demand for disposable cookware and the change in the average income of the population per month, the change in demand for this cookware and the change in the number of people who understand the essence of global problems comprising the humanity frame by having an active social position, the change in demand for disposable cookware with changes in price and product are also researched. Digital material and empirical data of Ukrainian enterprises are used in this study.