Factor copula approaches for assessing spatially dependent high-dimensional risks. (English) Zbl 07059859

Summary: In this article, we propose an innovative approach for modeling spatial dependence among losses from various geographical locations. The proposed model converts the challenging task of modeling complex spatial dependence structures into a relatively easier task of estimating a continuous function, of which the arguments can be the coordinates of the locations. The approach is based on factor copula models, which can capture various linear and nonlinear dependence. We use radial basis functions as the kernel smoother for estimating the key function that models all the spatial dependence structures. A case study on a thunderstorm wind loss dataset demonstrates the analysis and the usefulness of the proposed approach. Extensions to spatiotemporal models and to models for discrete data are briefly introduced, with an example given for modeling loss frequency with excess zeros.


91-XX Game theory, economics, finance, and other social and behavioral sciences
62-XX Statistics


Full Text: DOI


[1] Aas, K.; Czado, C.; Frigessi, A.; Bakken, H., Pair-Copula Constructions of Multiple Dependence, Insurance: Mathematics and Economics, 44, 2, 182-198, (2009) · Zbl 1165.60009
[2] Bárdossy, A., Copula-Based Geostatistical Models for Groundwater Quality Parameters, Water Resources Research, 42, 11, 1-12, (2006)
[3] Bedford, T.; Cooke, R. M., Vines—A New Graphical Model for Dependent Random Variables, Annals of Statistics, 30, 4, 1031-1068, (2002) · Zbl 1101.62339
[4] Cooke, R. M., Markov and Entropy Properties of Tree-and Vine-Dependent Variables, Proceedings of the ASA Section of Bayesian Statistical Science, 27, (1997)
[5] Cressie, N., Statistics for Spatial Data, (1993), New York: John Wiley & Sons, New York
[6] Cressie, N.; Wikle, C. K., Statistics for Spatio-temporal Data, (2011), New York: John Wiley & Sons, New York · Zbl 1273.62017
[7] Ebrahimi, N.; Hua, L., Assessing the Reliability of a Nanocomponent by Using Copulas, IIE Transactions, 46, 11, 1196-1208, (2014)
[8] Erhardt, T. M.; Czado, C.; Schepsmeier, U., R-Vine Models for Spatial Time Series with an Application to Daily Mean Temperature, Biometrics, 71, 2, 323-332, (2015) · Zbl 1390.62326
[9] Erhardt, T. M.; Czado, C.; Schepsmeier, U., Journal of Multivariate Analysis, 138, Spatial Composite Likelihood Inference Using Local c-Vines, 74-88, (2015) · Zbl 1328.62324
[10] Gräler, B.; Pebesma, E., The Pair-Copula Construction for Spatial Data: A New Approach to Model Spatial Dependency, Procedia Environmental Sciences, 7, 206-211, (2011)
[11] Joe, H., Multivariate Extreme-Value Distributions with Applications to Environmental Data, Canadian Journal of Statistics, 22, 1, 47-64, (1994) · Zbl 0804.62052
[12] Joe, H., Dependence Modeling with Copulas, (2014), New York: Chapman & Hall, New York · Zbl 1346.62001
[13] Journel, A. G.; Huijbregts, C. J., Mining Geostatistics, (1978), San Diego: Academic press, San Diego
[14] Krupskii, P.; Joe, H., Journal of Multivariate Analysis, 120, Factor Copula Models for Multivariate Data, 85-101, (2013) · Zbl 1280.62070
[15] Krupskii, P.; Joe, H., Journal of Multivariate Analysis, 138, Structured Factor Copula Models: Theory, Inference and Computation, 53-73, (2015) · Zbl 1320.62139
[16] Kurowicka, D.; Joe, H., Dependence Modeling: Vine Copula Handbook, (2011), Singapore: World Scientific, Singapore
[17] Mongillo, M., SIAM Undergraduate Research Online, 4, Choosing Basis Functions and Shape Parameters for Radial Basis Function Methods, 190-209, (2011)
[18] Nikoloulopoulos, A. K.; Joe, H., Factor Copula Models for Item Response Data, Psychometrika, 80, 1, 126-150, (2013) · Zbl 1314.62276
[19] Sklar, A., Publications de l’Institut de statistique de l’Universite’ de Paris, 8, Fonctions de répartition à n dimensions et leurs marges, 229-231, (1959)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.