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Copulae: an overview and recent developments. (English) Zbl 07910971

MSC:

62-08 Computational methods for problems pertaining to statistics

Software:

CopulaModel

References:

[1] Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). Pair‐copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44(2), 182-198. · Zbl 1165.60009
[2] Acar, E. F., Czado, C., & Lysy, M. (2019). Flexible dynamic vine copula models for multivariate time series data. Econometrics and Statistics, 12, 181-197.
[3] Ahmadabadi, A., & Ucer, B. H. (2017). Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach. Computational Statistics, 32, 1515-1532. · Zbl 1417.62139
[4] Andersen, L. N., Laub, P. J., & Rojas‐Nandayapa, L. (2018). Efficient simulation for dependent rare events with applications to extremes. Methodology and Computing in Applied Probability, 20, 385-409. · Zbl 1385.65014
[5] Aulbach, S., Bayer, V., & Falk, M. (2012). Multivariate piecing‐together approach with an application to operational loss data. Bernoulli, 18(2), 455-475. · Zbl 1238.62062
[6] Aulbach, S., Falk, M., & Fuller, T. (2019). Testing for a_δ‐neighbourhood of a generalized Pareto copula. Annals of the Institute of Statistical Mathematics, 71, 599-626. · Zbl 1422.62174
[7] Bacigal, T., Jagr, V., & Mesiar, R. (2011). Non‐exchangeable random variables, Archimax copulas and their fitting to real data. Kybernetika, 47(4), 519-531. · Zbl 1227.93120
[8] Beare, B. K. (2010). Copulas and temporal dependence. Econometrica, 78(1), 395-410. · Zbl 1202.91271
[9] Beare, B. K. (2012). Archimedean copulas and temporal dependence. Econometric Theory, 28(6), 1165-1185. · Zbl 1281.62143
[10] Beare, B. K., & Seo, J. (2015). Vine copula specifications for stationary multivariate Markov chains. Journal of Time Series Analysis, 36(2), 228-246. · Zbl 1320.62224
[11] Beare, B. K., & Seo, J. (2020). Randomization tests of copula symmetry. Econometric Theory, 36(6), 1025-1063. · Zbl 1462.62297
[12] Bedford, T., & Cooke, R. M. (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32, 245-268. · Zbl 1314.62040
[13] Bedford, T., & Cooke, R. M. (2002). Vines: A new graphical model for dependent random variables. Annals of Statistics, 30(4), 1031-1068. · Zbl 1101.62339
[14] Bhat, C. R., & Eluru, N. (2009). A copula‐based approach to accommodate residential self‐selection effects in travel behavior modeling. Transportation Research Part B: Methodological, 43(7), 749-765.
[15] Bianchi, P., Elgui, K., and Portier, F. (2020). Conditional independence testing via weighted partial copulas. Working Paper. https://arxiv.org/pdf/2006.12839.pdf
[16] Blumentritt, T., & Schmid, F. (2012). Mutual information as a measure of multivariate association: Analytical properties and statistical estimation. Journal of Statistical Computation and Simulation, 82(9), 1257-1274. · Zbl 1431.62248
[17] Blumentritt, T., & Schmid, F. (2014). Nonparametric estimation of copula‐based measures of multivariate association from contingency tables. Journal of Statistical Computation and Simulation, 84(4), 781-797. · Zbl 1453.62527
[18] Botev, Z. I., L’Ecuyer, P., Simard, R., & Tuffin, B. (2016). Static network reliability estimation under the Marshall‐Olkin copula. ACM Transactions on Modeling and Computer Simulation, 26(2), 1-28. · Zbl 1369.90057
[19] Brechmann, E. C. (2014). Hierarchical Kendall copulas: Properties and inference. The Canadian Journal of Statistics, 42(1), 78-108. · Zbl 1349.62172
[20] Breymann, W., Dias, A., & Embrechts, P. (2003). Dependence structures for multivariate high‐frequency data in finance. Quantitative Finance, 3(1), 1-14. · Zbl 1408.62173
[21] Bukovsek, D. K., Kosir, T., Mojskerc, B., and Omladic, M. (2019). Relation between Blomqvist’s beta and other measures of concordance of copulas. Working Paper. https://arxiv.org/pdf/1911.03467.pdf
[22] Capéràa, P., Fougères, A.‐L., & Genest, C. (1997). A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika, 84(3), 567-577. · Zbl 1058.62516
[23] Capéràa, P., Fougères, A.‐L., & Genest, C. (2000). Bivariate distributions with given extreme value attractor. Journal of Multivariate Analysis, 72(1), 30-49. · Zbl 0978.62043
[24] Carrera, D., Bandeira, L., Santana, R., & Lozano, J. A. (2019). Detection of sand dunes on mars using a regular vine‐based classification approach. Knowledge‐Based Systems, 163, 858-874.
[25] Chang, B., Pan, S., & Joe, H. (2019). Vine copula structure learning via Monte Carlo tree search. Proceedings of Machine Learning Research, 89, 353-361.
[26] Charpentier, A., Fougères, A.‐L., Genest, C., & Nešlehová, J. G. (2014). Multivariate Archimax copulas. Journal of Multivariate Analysis, 126, 118-136. · Zbl 1349.62173
[27] Chatelain, S., Fougères, A.‐L., & Nešlehová, J. G. (2020). Inference for Archimax copulas. The Annals of Statistics, 48(2), 1025-1051. · Zbl 1450.62046
[28] Chatrabgoun, O., Parham, G., & Chinipardaz, R. (2017). A Legendre multiwavelets approach to copula density estimation. Statistical Papers, 58, 673-690. · Zbl 1387.62071
[29] Chen, R.‐B., Guo, M., Härdle, W., & Huang, S.‐F. (2015). COPICA: Independent component analysis via copula techniques. Statistics and Computing, 25, 273-288. · Zbl 1331.65027
[30] Chen, X., & Fan, Y. (2006). Estimation and model selection of semiparametric copula‐based multivariate dynamic models under copula misspecification. Journal of Econometrics, 135(1-2), 125-154. · Zbl 1418.62425
[31] Chen, X., Fan, Y., and Patton, A. (2004). Simple tests for models of dependence between multiple financial time series, with applications to U.S. equity returns and exchange rates. Discussion paper 483, Financial Markets Group, London School of Economics.
[32] Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copula methods in finance. John Wiley & Sons. · Zbl 1163.62081
[33] Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65(1), 141-151. · Zbl 0394.92021
[34] Cossette, H., Marceau, E., Nguyen, Q. H., & Robert, C. Y. (2019). Tail approximation for sums of dependent regularly varying random variables under Archimedean copula models. Methodology and Computing in Applied Probability, 21, 461-490. · Zbl 1480.60140
[35] Deheuvels, P. (1979). La fonction de dépendance empirique et ses propriétés. un test non paramétrique d’indépendance. Bulletin de la Classe des Sciences, 65, 274-292. · Zbl 0422.62037
[36] Deldossi, L., Osmetti, S. A., & Tomassi, C. (2019). Optimal design to discriminate between rival copula models for a bivariate binary response. TEST, 28, 147-165. · Zbl 1420.62327
[37] Demarta, S., & McNeil, A. J. (2005). The t copula and related copulas. International Statistical Review, 73(1), 111-129. · Zbl 1104.62060
[38] Disegna, M., D’Urso, P., & Durante, F. (2017). Copula‐based fuzzy clustering of spatial time series. Spatial Statistics, 21, 209-225.
[39] Dokuzoğlu, D., & Purutçuoğlu, V. (2017). Comprehensive analyses of Gaussian graphical model under different biological networks. Acta Physica Polonica, A, 132(3), 1106-1111.
[40] Durante, F., Girard, S., & Mazo, G. (2015). Copulas based on Marshall‐Olkin machinery. In U.Cherubini (ed.), F.Durante (ed.), & S.Mulinacci (ed.) (Eds.), Marshall Olkin distributions: Advances in theory and applications (pp. 15-31). Springer. · Zbl 1365.62188
[41] Durante, F., Girard, S., & Mazo, G. (2016). Marshall‐Olkin type copulas generated by a global shock. Journal of Computational and Applied Mathematics, 296, 638-648. · Zbl 1328.62305
[42] Durante, F., & Sempi, C. (2010). Copula theory: An introduction. In P.Jaworski (ed.), F.Durante (ed.), W. K.Härdle (ed.), & T.Rychlik (ed.) (Eds.), Copula theory and its applications (pp. 3-31). Springer.
[43] Durante, F., & Sempi, C. (2015). Principles of copula theory. Chapman and Hall/CRC.
[44] Elidan, G. (2013). Copulas in machine learning. In Proceedings of the Workshop on Copulae in Mathematical and Quantitative Finance.
[45] Embrechts, P., McNeil, A. J., & Straumann, D. (2002). Correlation and dependence in risk management: Properties and pitfalls. In M. A. H.Dempster (ed.) (Ed.), Risk management (pp. 176-223). Cambridge University Press.
[46] Falk, M., Hüsler, J., & Reiss, R.‐D. (2011). Laws of small numbers: Extremes and rare events. Springer. · Zbl 1213.62082
[47] Falk, M., Padoan, S. A., & Wisheckel, F. (2019). Generalized pareto copulas: A key to multivariate extremes. Journal of Multivariate Analysis, 174, 174-212. · Zbl 1428.62200
[48] Fengler, M. R., & Okhrin, O. (2016). Managing risk with a realized copula parameter. Computational Statistics and Data Analysis, 100, 131-152. · Zbl 1466.62065
[49] Fermanian, J.‐D. (2005). Goodness‐of‐fit tests for copulas. Journal of Multivariate Analysis, 95(1), 119-152. · Zbl 1095.62052
[50] Fermanian, J.‐D., Radulovic, D., & Wegkamp, M. (2004). Weak convergence of empirical copula processes. Bernoulli, 10(5), 847-860. · Zbl 1068.62059
[51] Fermanian, J.‐D., & Scaillet, O. (2003). Nonparametric estimation of copulas for time series. Risk, 5(4), 25-54.
[52] Frank, M. J. (1979). On the simultaneous associativity of f(x,y) and x+y‐f(x,y). Aequationes mathematicae, 19, 194-226. · Zbl 0444.39003
[53] Gaensler, P., & Stute, W. (1987). Seminar on empirical processes. Springer Basel AG. · Zbl 0637.62047
[54] Genest, C., Carabarín‐Aguirre, A., & Harvey, F. (2013). Copula parameter estimation using Blomqvist’s beta. Journal de la Société Française de Statistique, 154(1), 5-24. · Zbl 1316.62069
[55] Genest, C., Ghoudi, K., & Rivest, L.‐P. (1995). A semi‐parametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82(3), 543-552. · Zbl 0831.62030
[56] Genest, C., & Jaworski, P. (2020). On the class of bivariate archimax copulas under constraints. Fuzzy Sets and Systems.
[57] Genest, C., Mesfioui, M., & Nešlehová, J. G. (2019a). On the asymptotic covariance of the multivariate empirical copula process. Dependence Modeling, 7, 279-291. · Zbl 1445.62103
[58] Genest, C., & Nešlehová, J. (2014). Copulas and copula models (statistics reference online). Wiley StatsRef.
[59] Genest, C., Nešlehová, J. G., & Rémillard, B. (2017). Asymptotic behavior of the empirical multiliniar copula process under broad conditions. Journal of Multivariate Analysis, 159, 82-110. · Zbl 1368.62036
[60] Genest, C., Nešlehová, J. G., Rémillard, B., & Murphy, O. A. (2019b). Testing for independence in arbitrary distributions. Biometrika, 106(1), 47-68. · Zbl 1506.62309
[61] Genest, C., Quessy, J.‐F., & Rémillard, B. (2006). Goodness‐of‐fit procedures for copula models based on the probability integral transformation. Scandinavian Journal of Statistics, 33(2), 337-366. · Zbl 1124.62028
[62] Genest, C., & Rémillard, B. (2008). Validity of the parametric bootstrap for goodness‐of‐fit testing in semiparametric models. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 44(6), 1096-1127. · Zbl 1206.62044
[63] Genest, C., Rémillard, B., & Beaudoin, D. (2009). Goodness‐of‐fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44(2), 199-213. · Zbl 1161.91416
[64] Genest, C., & Rivest, L.‐P. (1989). A characterization of Gumbel family of extreme value distributions. Statistics & Probability Letters, 8(3), 207-211. · Zbl 0701.62060
[65] Genest, C., & Rivest, L.‐P. (1993). Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88(423), 1034-1043. · Zbl 0785.62032
[66] Gomes, M., Radice, R., Camarena Brenes, J., & Marra, G. (2019). Copula selection models for non‐Gaussian outcomes that are missing not at random. Statistics in Medicine, 38(3), 480-496.
[67] Górecki, J., Hofert, M., & Holeňa, M. (2016). An approach to structure determination and estimation of hierarchical Archimedean copulas and its application to Bayesian classification. Journal of Intelligent Information Systems, 46, 21-59.
[68] Górecki, J., Hofert, M., & Holeňa, M. (2017a). Kendall’s tau and agglomerative clustering. Dependence Modeling, 5, 75-87. · Zbl 1404.62054
[69] Górecki, J., Hofert, M., & Holeňa, M. (2017b). On structure, family and parameter estimation of hierarchical Archimedean copulas. Journal of Statistical Computation and Simulation, 87(17), 3261-3324. · Zbl 07192120
[70] Górecki, J., Hofert, M., & Okhrin, O. (2021). Outer power transformations of hierarchical Archimedean copulas: Construction, sampling and estimation. Computational Statistics and Data Analysis, 155. · Zbl 1510.62227
[71] Gudendorf, G., & Segers, J. (2010). Extreme‐value copulas. In P.Jaworski (ed.), F.Durante (ed.), W. K.Härdle (ed.), & T.Rychlik (ed.) (Eds.), Copula theory and its applications (pp. 127-145). Springer.
[72] Gumbel, E. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292), 698-707. · Zbl 0099.14501
[73] Gunawan, D., Tran, M.‐N., Suzuki, K., Dick, J., & Kohn, R. (2019). Computationally efficient Bayesian estimation of high‐dimensional Archimedean copulas. Statistics and Computing, 29, 933-946. · Zbl 1430.62101
[74] Haff, I. H. (2013). Parameter estimation for pair‐copula constructions. Bernoulli, 19(2), 462-491. · Zbl 1456.62033
[75] Härdle, W. K., Okhrin, O., & Okhrin, Y. (2013). Dynamic structured copula models. Statistics and Risk Modeling, 30, 361-388. · Zbl 1279.62185
[76] Härdle, W. K., Okhrin, O., & Wang, W. (2015). Hidden Markov structures for dynamic copulae. Econometric Theory, 31(5), 981-1015. · Zbl 1441.62723
[77] Härdle, W. K., & Simar, L. (2015). Applied multivariate statistical analysis. Springer. · Zbl 1308.62002
[78] Hofert, M. (2011). Efficiently sampling nested Archimedean copulas. Computational Statistics & Data Analysis, 55(1), 57-70. · Zbl 1247.62132
[79] Hofert, M., Kojadinovic, I., Maechler, M., & Yan, J. (2018). Elements of copula modeling with R. Springer Use R! Series. · Zbl 1412.62004
[80] Hofert, M., & Scherer, M. (2011). CDO pricing with nested Archimedean copulas. Quantitative Finance, 11(5), 775-787. · Zbl 1213.91074
[81] Huang, K., Dai, L., Yao, M., Fan, Y., & Kong, X. (2017). Modelling dependence between traffic noise and traffic flow through an entropy‐copula method. Journal of Environmental Informatics, 29(2), 134-151.
[82] Hyvärinen, A. (2012). Independent component analysis: Recent advances. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, 1-19. · Zbl 1353.62066
[83] Isomura, T., & Toyoizumi, T. (2016). A local learning rule for independent component analysis. Scientific Reports, 6, 1-17.
[84] Joe, H. (1996). Families of m‐variate distributions with given margins and m(m‐1)/2 bivariate dependence parameters. In L.Rüschendorf (ed.), B.Schweizer (ed.), & M.Taylor (ed.) (Eds.), Distribution with fixed marginals and related topics, IMS lecture notes - Monograph series. Institute of Mathematical Statistics.
[85] Joe, H. (1997). Multivariate models and dependence concepts. Chapman & Hall. · Zbl 0990.62517
[86] Joe, H. (2014). Dependence modeling with copulas. Chapman and Hall/CRC. · Zbl 1346.62001
[87] Joe, H., & Sang, P. (2016). Multivariate models for dependent clusters of variables with conditional independence given aggregation variables. Computational Statistics and Data Analysis, 97, 114-132. · Zbl 1468.62094
[88] Kamnitui, N., Genest, C., Jaworski, P., & Trutschnig, W. (2019). On the size of the class of bivariate extreme‐value copulas with a fixed value of Spearman’s ρ or Kendall’s τ. Journal of Mathematical Analysis and Applications, 472(1), 920-936. · Zbl 1418.62224
[89] Karra, K. and Mili, L. (2016). Hybrid copula Bayesian networks. In Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR (pp. 240-251).
[90] Kilgore, R. T., & Thompson, D. B. (2011). Estimating joint flow probabilities at stream confluences by using copulas. Transportation Research Record, 2262, 200-206.
[91] Killiches, M., Kraus, D., & Czado, C. (2018). Model distances for vine copulas in high dimensions. Statistics and Computing, 28, 323-341. · Zbl 1384.62168
[92] Kim, S., Kim, K.‐K., & Ryu, H. (2020). Robust quantile estimation under bivariate extreme value models. Extremes, 23, 55-83. · Zbl 1471.62355
[93] Kiriliouk, A., Segers, J., & Tafakori, L. (2018). An estimator of the stable tail dependence function based on the empirical beta copula. Extremes, 21, 581-600. · Zbl 1410.62073
[94] Kole, E., Koedijk, K., & Verbeek, M. (2007). Selecting copulas for risk management. Journal of Banking and Finance, 31(8), 2405-2423.
[95] Konigorski, S., Yilmaz, Y. E., & Bull, S. B. (2014). Bivariate genetic association analysis of systolic and diastolic blood pressure by copula models. BMC Proceedings, 8(1), S72.
[96] Kraus, D., & Czado, C. (2017). D‐vine copula based quantile regression. Computational Statistics and Data Analysis, 110, 1-18. · Zbl 1466.62118
[97] Kreuzer, A. and Czado, C. (2019). Bayesian inference for dynamic vine copulas in higher dimensions. https://arxiv.org/abs/1911.00702
[98] Krupskii, P., & Joe, H. (2013). Factor copula models for multivariate data. Journal of Multivariate Analysis, 120, 85-101. · Zbl 1280.62070
[99] Krupskii, P., & Joe, H. (2015). Structured factor copula models: Theory, inference and computation. Journal of Multivariate Analysis, 138, 53-73. · Zbl 1320.62139
[100] Kurowicka, M., & Cooke, R. M. (2006). Uncertainty analysis with high dimensional dependence Modelling. John Wiley & Sons. · Zbl 1096.62073
[101] Kuss, O., Hoyer, A., & Solms, A. (2014). Meta‐analysis for diagnostic accuracy studies: A new statistical model using beta‐binomial distributions and bivariate copulas. Statistics in Medicine, 33(1), 17-30.
[102] Lapuyade‐Lahorgue, J., Xue, J.‐H., & Ruan, S. (2017). Segmenting multi‐source images using hidden Markov fields with copula‐based multivariate statistical distributions. IEEE Transactions on Image Processing, 26(7), 3187-3195. · Zbl 1409.94315
[103] Li, D. X. (2000). On default correlation: A copula function approach. Journal of Fixed Income, 9(4), 43-54.
[104] Lin, J., & Li, X. (2014). Multivariate generalized Marshall‐Olkin distributions and copulas. Methodology and Computing in Applied Probability, 16, 53-78. · Zbl 1291.60031
[105] Lin, J.‐G., Zhang, K.‐S., & Zhao, Y.‐Y. (2017). Nonparametric estimation of multivariate multiparameter conditional copulas. Journal of the Korean Statistical Society, 46(1), 126-136. · Zbl 1360.62182
[106] Liu, Z., Guo, S., Xiong, L., & Xu, C.‐Y. (2018). Hydrological uncertainty processor based on a copula function. Hydrological Sciences Journal, 63(1), 74-86.
[107] Luca, G. D., & Zuccolotto, P. (2017). Dynamic tail dependence clustering of financial time series. Statistical Papers, 58, 641-657. · Zbl 1416.62581
[108] Luo, X., & Shevchenko, P. V. (2010). The t‐copula with multiple parameters of degrees of freedom: Bivariate characteristics and application to risk management. Quantitative Finance, 10(9), 1039-1054. · Zbl 1210.91060
[109] Ma, J., & Sun, Z. (2007). Copula component analysis. In M. E.Davies (ed.), C. J.James (ed.), S. A.Abdallah (ed.), & M. D.Plumbley (ed.) (Eds.), Independent component analysis and signal separation (pp. 73-80). Springer. · Zbl 1172.94453
[110] Ma, X., Luan, S., Du, B., & Yu, B. (2017). Spatial copula model for imputing traffic flow data from remote microwave sensors. Sensors, 17(10), 2160.
[111] Mai, J.‐F., & Scherer, M. (2012). Simulating copulas: Stochastic models, sampling algorithms, and applications. Imperial College Press. · Zbl 1301.65001
[112] Marshall, A. W., & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association, 62(317), 30-44. · Zbl 0147.38106
[113] Mesiar, R., & Jágr, V. (2013). d‐dimensional dependence functions and Archimax copulas. Fuzzy Sets and Systems, 228, 78-87. · Zbl 1284.62345
[114] Müller, D., & Czado, C. (2019). Selection of sparse vine copulas in high dimensions with the LASSO. Statistics and Computing, 29, 269-287. · Zbl 1430.62102
[115] Mulinacci, S. (2018). Archimedean‐based Marshall‐Olkin distributions and related dependence structures. Methodology and Computing in Applied Probability, 20, 205-236. · Zbl 1392.62047
[116] Nelsen, R. (2006). An introduction to copulas. Springer. · Zbl 1152.62030
[117] Neumann, A., & Dickhaus, T. (2020). Nonparametric Archimedean generator estimation with implications for multiple testing. AStA Advances in Statistical Analysis, 104, 309-323. · Zbl 1457.62102
[118] Nikoloulopoulos, A., & Joe, H. (2015). Factor copula models for item response data. Psychometrika, 80, 126-150. · Zbl 1314.62276
[119] Oh, D. H., & Patton, A. (2013). Simulated method of moments estimation for copula‐based multivariate models. Journal of the American Statistical Association, 108(502), 689-700. · Zbl 06195971
[120] Oh, D. H., & Patton, A. (2015). Modelling dependence in high dimensions with factor copulas. In Finance and economics discussion series 2015-051. Board of Governors of the Federal Reserve System.
[121] Oh, D. H., & Patton, A. J. (2018). Time‐varying systemic risk: Evidence from a dynamic copula model of CDS spreads. Journal of Business and Economic Statistics, 36(2), 181-195.
[122] Okhrin, O., Okhrin, Y., & Schmid, W. (2013a). On the structure and estimation of hierarchical Archimedean copulas. Journal of Econometrics, 173(2), 189-204. · Zbl 1443.62137
[123] Okhrin, O., Okhrin, Y., & Schmid, W. (2013b). Properties of hierarchical Archimedean copulas. Statistics & Risk Modeling, 30, 21-53. · Zbl 1348.62044
[124] Okhrin, O., & Ristig, A. (2014). Hierarchical Archimedean copulae: The HAC package. Journal of Statistical Software, 58(4), 1-20.
[125] Okhrin, O., Ristig, A., & Xu, Y.‐F. (2017). Copulae in high dimensions: An introduction. In W. K.Härdle (ed.), C. Y.‐H.Chen (ed.), & L.Overbeck (ed.) (Eds.), Applied quantitative finance. Springer.
[126] Oppenheimer, M., Little, C. M., & Cooke, R. M. (2016). Expert judgement and uncertainty quantification for climate change. Nature Climate Change, 6, 445-451.
[127] Ozdemir, O., Allen, T. G., Choi, S., Wimalajeewa, T., & Varshney, P. K. (2018). Copula based classifier fusion under statistical dependence. IEEE Transactions on Pattern Analysis and Machine Intelligence, 40(11), 2740-2748.
[128] Patton, A. J. (2004). On the out‐of‐sample importance of skewness and asymmetric dependence for asset allocation. Journal of Financial Econometrics, 2(1), 130-168.
[129] Patton, A. J. (2006). Modelling asymmetric exchange rate dependence. International Economic Review, 47(2), 527-556.
[130] Patton, A. J. (2012). A review of copula models for economic time series. Journal of Multivariate Analysis, 110, 4-18. · Zbl 1244.62085
[131] Pickands, J. (1981). Multivariate extreme value distributions. In Proceedings of the 43rd session of the International Statistical Institute (pp. 245-253). · Zbl 0515.00023
[132] Pircalabelu, E., Claeskens, G., & Gijbels, I. (2017). Copula directed acyclic graphs. Statistics and Computing, 27, 55-78. · Zbl 1505.62322
[133] Quessy, J.‐F. (2019). Consistent nonparametric tests for detecting gradual changes in the marginals and the copula of multivariate time series. Statistical Papers, 60, 717-746. · Zbl 1419.62244
[134] Rachev, S., Stoyanov, S., & Fabozzi, F. (2008). Advanced stochastic models, risk assessment, and portfolio optimization: The ideal risk, uncertainty, and performance measures. John Wiley & Sons.
[135] Rey, M. (2015). Copula models in machine learning (PhD Thesis). Universität Basel.
[136] Rojo, J., Villa‐Diharce, E., & Flores, M. (2001). Nonparametric estimation of the dependence function in bivariate extreme value distributions. Journal of Multivariate Analysis, 76(2), 159-191. · Zbl 0998.62050
[137] Rosenblatt, M. (1952). Remarks on a multivariate transformation. Annals of Mathematical Statistics, 23(3), 470-472. · Zbl 0047.13104
[138] Salvadori, G., Michele, C. D., Kottegoda, N. T., and Rosso, R. (2007). Extremes in nature. Berlin/Heidelberg: Springer.
[139] Salvatierra, I. D. L., & Patton, A. J. (2015). Dynamic copula models and high frequency data. Journal of Empirical Finance, 30, 120-135.
[140] Sancetta, A., & Satchell, S. (2004). The Bernstein copula and its applications to modeling and approximations of multivariate distributions. Econometric Theory, 20(3), 535-562. · Zbl 1061.62080
[141] Scaillet, O. (2007). Kernel‐based goodness‐of‐fit tests for copulas with fixed smoothing parameters. Journal of Multivariate Analysis, 98(3), 533-543. · Zbl 1107.62037
[142] Schefzik, R. (2015). Multivariate discrete copulas, with applications in probabilistic weather forecasting. Heidelberger Institut für Theoretische Studien. · Zbl 1317.86002
[143] Schellhase, C., & Spanhel, F. (2018). Estimating non‐simplified vine copulas using penalized splines. Statistics and Computing, 28, 387-409. · Zbl 1384.62170
[144] Schifano, E. D., Jeong, H., Deshpande, V., & Dey, E. K. (2020). Fully and empirical Bayes approaches to estimating copula‐based models for bivariate mixed outcomes using Hamiltonian Monte Carlo. TEST.
[145] Schölzel, C., & Friederichs, P. (2008). Multivariate non‐normally distributed random variables in climate research: Introduction to the copula approach. Nonlinear Processes in Geophysics, 15(5), 761-772.
[146] Schmid, F., & Schmidt, R. (2006). Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence. Metrika, 66, 323-354. · Zbl 1433.62151
[147] Schmid, F., & Schmidt, R. (2007). Multivariate extensions of Spearman’s rho and related statistics. Statistics and Probability Letters, 77(4), 407-416. · Zbl 1108.62056
[148] Schreyer, M., Paulin, R., & Trutschnig, W. (2017). On the exact region determined by Kendall’s τ and Spearman’s ρ. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79(2), 613-633. · Zbl 1414.62202
[149] Schweizer, B. (1991). Thirty years of copulas. Springer. · Zbl 0727.60001
[150] Schweizer, B., & Sklar, A. (1983). Probabilistic metric spaces. North‐Holland Publishing Co. · Zbl 0546.60010
[151] Segers, J., Sibuya, M., & Tsukahara, H. (2017). The empirical beta copula. Journal of Multivariate Analysis, 155, 35-51. · Zbl 1360.62237
[152] Segers, J., & Uyttendaele, N. (2014). Nonparametric estimation of the tree structure of a nested Archimedean copula. Computational Statistics & Data Analysis, 72, 190-204. · Zbl 1506.62163
[153] Sklar, A. (1959). Fonctions de répartition à n dimension et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris, 8, 299-231.
[154] Sraj, M., Bezak, N., & Brilly, M. (2014). Bivariate flood frequency analysis using the copula function: A case study of the Litija station on the Sava river. Hydrological Processes, 29(2), 225-238.
[155] Stöber, J., & Czado, C. (2012). Detecting regime switches in the dependence structure of high dimensional financial data. arXiv Preprint.
[156] Su, C.‐L., Nešlehová, J. G., & Wang, W. (2019). Modelling hierarchical clustered censored data with the hierarchical Kendall copula. The Canadian Journal of Statistics, 47(2), 182-203. · Zbl 1466.62399
[157] Susam, S. O., & Ucer, B. H. (2018). Testing independence for Archimedean copula based on Bernstein estimate of Kendall distribution function. Journal of Statistical Computation and Simulation, 88(13), 2589-2599. · Zbl 07192676
[158] Susam, S. O., & Ucer, B. H. (2020). A goodness‐of‐fit test based on Bezier curve estimation of Kendall distribution. Journal of Statistical Computation and Simulation, 90(7), 1194-1215. · Zbl 07194334
[159] Torre, E., Marelli, S., Embrechts, P., & Sudret, B. (2019). A general framework for data‐driven uncertainty quantification under complex input dependencies using vine copulas. Probabilistic Engineering Mechanics, 55, 1-16.
[160] Valle, D., & Kaplan, D. (2019). Quantifying the impacts of dams on riverine hydrology under non‐stationary conditions using incomplete data and Gaussian copula models. Science of the Total Environment, 677, 599-611.
[161] Vettori, S., Huser, R., & Genton, M. G. (2017). A comparison of dependence function estimators in multivariate extremes. Statistics and Computing, 28, 525-538. · Zbl 1384.62163
[162] Wang, W., & Wells, M. (2000). Model selection and semiparametric inference for bivariate failure‐time data. Journal of the American Statistical Association, 95(449), 62-72. · Zbl 0996.62091
[163] Wieczorek, A., Wieser, M., Murezzan, D., and Roth, V. (2018). Learning sparse latent representations with the deep copula information bottleneck. In: International Conference on Learning Representations.
[164] Wysocki, W. (2013). When a copula is Archimax. Statistics and Probability Letters, 83(1), 37-45. · Zbl 1452.62358
[165] Zhang, L., & Baek, J. (2019). Mixtures of Gaussian copula factor analyzers for clustering high dimensional data. Journal of the Korean Statistical Society, 48(3), 480-492. · Zbl 1428.62301
[166] Zhang, L., Lu, D., & Wang, X. (2020). Measuring and testing interdependence among random vectors based on Spearman’s ρ and Kendall’s τ. Computational Statistics, 35, 1685-1713. · Zbl 1505.62441
[167] Zhang, M., & Beford, T. (2018). Vine copula approximation: A generic method for coping with conditional dependence. Statistics and Computing, 28, 219-237. · Zbl 1384.62171
[168] Zhang, S., Geng, B., Varshney, P. K., and Rangaswamy, M. (2019). Fusion of deep neural networks for activity recognition: A regular vine copula based approach. In 2019 22th International Conference on Information FUSION (FUSION) (pp. 1-7).
[169] Zhang, S., Okhrin, O., Zhou, Q. M., & Song, P. X.‐K. (2016). Goodness‐of‐fit test for specification of semiparametric copula dependence models. Journal of Econometrics, 193(1), 215-233. · Zbl 1420.62210
[170] Zhu, K., Kurowicka, D., & Nane, G. F. (2020). Common sampling orders of regular vines with application to model selection. Computational Statistics and Data Analysis, 142, 106811. · Zbl 1507.62212
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