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2018 | OriginalPaper | Buchkapitel

5. Graphical Diagnostics, Tests, and Model Selection

verfasst von : Marius Hofert, Ivan Kojadinovic, Martin Mächler, Jun Yan

Erschienen in: Elements of Copula Modeling with R

Verlag: Springer International Publishing

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Abstract

This chapter presents graphical diagnostics and statistical tests, and discusses model selection for copulas.

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Literatur
Zurück zum Zitat Ben Ghorbal, M., Genest, C., & Nešlehová, J. G. (2009). On the test of Ghoudi, Khoudraji, and Rivest for extreme-value dependence. The Canadian Journal of Statistics, 37(4), 534–552.MathSciNetCrossRef Ben Ghorbal, M., Genest, C., & Nešlehová, J. G. (2009). On the test of Ghoudi, Khoudraji, and Rivest for extreme-value dependence. The Canadian Journal of Statistics, 37(4), 534–552.MathSciNetCrossRef
Zurück zum Zitat Berg, D. (2009). Copula goodness-of-fit testing: An overview and power comparison. The European Journal of Finance, 15, 675–701.CrossRef Berg, D. (2009). Copula goodness-of-fit testing: An overview and power comparison. The European Journal of Finance, 15, 675–701.CrossRef
Zurück zum Zitat Bücher, A., Dette, H., & Volgushev, S. (2012). A test for Archimedeanity in bivariate copula models. Journal of Multivariate Analysis, 110, 121–132.MathSciNetCrossRef Bücher, A., Dette, H., & Volgushev, S. (2012). A test for Archimedeanity in bivariate copula models. Journal of Multivariate Analysis, 110, 121–132.MathSciNetCrossRef
Zurück zum Zitat Bücher, A., & Kojadinovic, I. (2015). An overview of nonparametric tests of extreme-value dependence and of some related statistical procedures. In D. Dey & J. Yan (Eds.) Extreme value modeling and risk analysis: Methods and applications (pp. 377–398). Boca Baton, FL: Chapman & Hall/CRC.CrossRef Bücher, A., & Kojadinovic, I. (2015). An overview of nonparametric tests of extreme-value dependence and of some related statistical procedures. In D. Dey & J. Yan (Eds.) Extreme value modeling and risk analysis: Methods and applications (pp. 377–398). Boca Baton, FL: Chapman & Hall/CRC.CrossRef
Zurück zum Zitat Chen, X., & Fan, Y. (2005). Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection. The Canadian Journal of Statistics, 33, 389–414.MathSciNetCrossRef Chen, X., & Fan, Y. (2005). Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection. The Canadian Journal of Statistics, 33, 389–414.MathSciNetCrossRef
Zurück zum Zitat Claeskens, G., & Hjort, N. L. (2008). Model selection and model averaging. London: Cambridge University Press.CrossRef Claeskens, G., & Hjort, N. L. (2008). Model selection and model averaging. London: Cambridge University Press.CrossRef
Zurück zum Zitat Deheuvels, P. (1981). A non parametric test for independence. Publications de l’Institut de Statistique de l’Université de Paris, 26, 29–50.MATH Deheuvels, P. (1981). A non parametric test for independence. Publications de l’Institut de Statistique de l’Université de Paris, 26, 29–50.MATH
Zurück zum Zitat Fermanian, J.-D. (2005). Goodness-of-fit tests for copulas. Journal of Multivariate Analysis, 95(1), 119–152.MathSciNetCrossRef Fermanian, J.-D. (2005). Goodness-of-fit tests for copulas. Journal of Multivariate Analysis, 95(1), 119–152.MathSciNetCrossRef
Zurück zum Zitat Fermanian, J.-D. (2013). An overview of the goodness-of-fit test problem for copulas. In P. Jaworski, F. Durante, & W. K. Härdle (Eds.), Copulae in mathematical and quantitative finance. Lectures notes in statistics (pp. 61–89). Berlin: Springer.CrossRef Fermanian, J.-D. (2013). An overview of the goodness-of-fit test problem for copulas. In P. Jaworski, F. Durante, & W. K. Härdle (Eds.), Copulae in mathematical and quantitative finance. Lectures notes in statistics (pp. 61–89). Berlin: Springer.CrossRef
Zurück zum Zitat Genest, C., & Boies, J.-C. (2003). Detecting dependence with Kendall plots. The American Statistician, 57, 275–284.MathSciNetCrossRef Genest, C., & Boies, J.-C. (2003). Detecting dependence with Kendall plots. The American Statistician, 57, 275–284.MathSciNetCrossRef
Zurück zum Zitat Genest, C., & Favre, A.-C. (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrological Engineering, 12, 347–368.CrossRef Genest, C., & Favre, A.-C. (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrological Engineering, 12, 347–368.CrossRef
Zurück zum Zitat Genest, C., Nešlehová, J., & Quessy, J.-F. (2012). Tests of symmetry for bivariate copulas. Annals of the Institute of Statistical Mathematics, 64, 811–834.MathSciNetCrossRef Genest, C., Nešlehová, J., & Quessy, J.-F. (2012). Tests of symmetry for bivariate copulas. Annals of the Institute of Statistical Mathematics, 64, 811–834.MathSciNetCrossRef
Zurück zum Zitat Genest, C., & Nešlehová, J. G. (2014). On tests of radial symmetry for bivariate copulas. Statistical Papers, 55, 1107–1119.MathSciNetCrossRef Genest, C., & Nešlehová, J. G. (2014). On tests of radial symmetry for bivariate copulas. Statistical Papers, 55, 1107–1119.MathSciNetCrossRef
Zurück zum Zitat Genest, C., Quessy, J.-F., & Rémillard, B. (2007). Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence. The Annals of Statistics, 35, 166–191.MathSciNetCrossRef Genest, C., Quessy, J.-F., & Rémillard, B. (2007). Asymptotic local efficiency of Cramér–von Mises tests for multivariate independence. The Annals of Statistics, 35, 166–191.MathSciNetCrossRef
Zurück zum Zitat Genest, C., & Rémillard, B. (2004). Tests of independence and randomness based on the empirical copula process. Test, 13(2), 335–369.MathSciNetCrossRef Genest, C., & Rémillard, B. (2004). Tests of independence and randomness based on the empirical copula process. Test, 13(2), 335–369.MathSciNetCrossRef
Zurück zum Zitat 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, 1096–1127.MathSciNetCrossRef 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, 1096–1127.MathSciNetCrossRef
Zurück zum Zitat Genest, C., Rémillard, B., & Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44, 199–213.MathSciNetMATH Genest, C., Rémillard, B., & Beaudoin, D. (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and Economics, 44, 199–213.MathSciNetMATH
Zurück zum Zitat Ghoudi, K., Khoudraji, A., & Rivest, L.-P. (1998). Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles. The Canadian Journal of Statistics, 26(1), 187–197.MathSciNetCrossRef Ghoudi, K., Khoudraji, A., & Rivest, L.-P. (1998). Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles. The Canadian Journal of Statistics, 26(1), 187–197.MathSciNetCrossRef
Zurück zum Zitat Grønneberg, S., & Hjort, N. L. (2014). The copula information criteria. Scandinavian Journal of Statistics, 41, 436–459.MathSciNetCrossRef Grønneberg, S., & Hjort, N. L. (2014). The copula information criteria. Scandinavian Journal of Statistics, 41, 436–459.MathSciNetCrossRef
Zurück zum Zitat Harder, M., & Stadtmüller, U. (2017). Testing exchangeability of copulas in arbitrary dimension. Journal of Nonparametric Statistics, 29(1), 40–60.MathSciNetCrossRef Harder, M., & Stadtmüller, U. (2017). Testing exchangeability of copulas in arbitrary dimension. Journal of Nonparametric Statistics, 29(1), 40–60.MathSciNetCrossRef
Zurück zum Zitat Hofert, M., & Mächler, M. (2014). A graphical goodness-of-fit test for dependence models in higher dimensions. Journal of Computational and Graphical Statistics, 23(3), 700–716.MathSciNetCrossRef Hofert, M., & Mächler, M. (2014). A graphical goodness-of-fit test for dependence models in higher dimensions. Journal of Computational and Graphical Statistics, 23(3), 700–716.MathSciNetCrossRef
Zurück zum Zitat Hofert, M., & Oldford, R. W. (2017). Visualizing dependence in high-dimensional data: An application to S&P 500 constituent data. Econometrics and Statistics, 8, 161–183.MathSciNetCrossRef Hofert, M., & Oldford, R. W. (2017). Visualizing dependence in high-dimensional data: An application to S&P 500 constituent data. Econometrics and Statistics, 8, 161–183.MathSciNetCrossRef
Zurück zum Zitat Joe, H. (2014). Dependence modeling with copulas. Boca Raton, FL: Chapman & Hall/CRC. Joe, H. (2014). Dependence modeling with copulas. Boca Raton, FL: Chapman & Hall/CRC.
Zurück zum Zitat Jordanger, L. A., & Tjøstheim, D. (2014). Model selection of copulas: AIC versus a cross validation copula information criterion. Statistics & Probability Letters, 92, 249–255.MathSciNetCrossRef Jordanger, L. A., & Tjøstheim, D. (2014). Model selection of copulas: AIC versus a cross validation copula information criterion. Statistics & Probability Letters, 92, 249–255.MathSciNetCrossRef
Zurück zum Zitat Kojadinovic, I. (2017). Some copula inference procedures adapted to the presence of ties. Computational Statistics and Data Analysis, 142, 24–41.MathSciNetCrossRef Kojadinovic, I. (2017). Some copula inference procedures adapted to the presence of ties. Computational Statistics and Data Analysis, 142, 24–41.MathSciNetCrossRef
Zurück zum Zitat Kojadinovic, I., & Holmes, M. (2009). Tests of independence among continuous random vectors based on Cramér–von Mises functionals of the empirical copula process. Journal of Multivariate Analysis, 100(6), 1137–1154.MathSciNetCrossRef Kojadinovic, I., & Holmes, M. (2009). Tests of independence among continuous random vectors based on Cramér–von Mises functionals of the empirical copula process. Journal of Multivariate Analysis, 100(6), 1137–1154.MathSciNetCrossRef
Zurück zum Zitat Kojadinovic, I., Segers, J., & Yan, J. (2011). Large-sample tests of extreme-value dependence for multivariate copulas. The Canadian Journal of Statistics, 39(4), 703–720.MathSciNetCrossRef Kojadinovic, I., Segers, J., & Yan, J. (2011). Large-sample tests of extreme-value dependence for multivariate copulas. The Canadian Journal of Statistics, 39(4), 703–720.MathSciNetCrossRef
Zurück zum Zitat Kojadinovic, I., & Yan, J. (2011). A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems. Statistics and Computing, 21(1), 17–30.MathSciNetCrossRef Kojadinovic, I., & Yan, J. (2011). A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems. Statistics and Computing, 21(1), 17–30.MathSciNetCrossRef
Zurück zum Zitat Kojadinovic, I., & Yan, J. (2012). A nonparametric test of exchangeability for extreme-value and left-tail decreasing bivariate copulas. Scandinavian Journal of Statistics, 39(3), 480–496.MathSciNetCrossRef Kojadinovic, I., & Yan, J. (2012). A nonparametric test of exchangeability for extreme-value and left-tail decreasing bivariate copulas. Scandinavian Journal of Statistics, 39(3), 480–496.MathSciNetCrossRef
Zurück zum Zitat Kojadinovic, I., Yan, J., & Holmes, M. (2011). Fast large-sample goodness-of-fit for copulas. Statistica Sinica, 21(2), 841–871.MathSciNetCrossRef Kojadinovic, I., Yan, J., & Holmes, M. (2011). Fast large-sample goodness-of-fit for copulas. Statistica Sinica, 21(2), 841–871.MathSciNetCrossRef
Zurück zum Zitat McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools (2nd ed.). Princeton, NJ: Princeton University Press.MATH McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools (2nd ed.). Princeton, NJ: Princeton University Press.MATH
Zurück zum Zitat Quessy, J.-F. (2005), Méthodologie et application des copules: tests d’adéquation, tests d’indépendance, et bornes sur la valeur-à-risque. PhD thesis, Université Laval, Québec, Canada. Quessy, J.-F. (2005), Méthodologie et application des copules: tests d’adéquation, tests d’indépendance, et bornes sur la valeur-à-risque. PhD thesis, Université Laval, Québec, Canada.
Zurück zum Zitat Rémillard, B., & Scaillet, O. (2009), Testing for equality between two copulas. Journal of Multivariate Analysis, 100(3), 377–386.MathSciNetCrossRef Rémillard, B., & Scaillet, O. (2009), Testing for equality between two copulas. Journal of Multivariate Analysis, 100(3), 377–386.MathSciNetCrossRef
Zurück zum Zitat Schmid, F., & Schmidt, R. (2007). Multivariate extensions of Spearman’s rho and related statistics. Statistics & Probability Letters, 77(4), 407–416.MathSciNetCrossRef Schmid, F., & Schmidt, R. (2007). Multivariate extensions of Spearman’s rho and related statistics. Statistics & Probability Letters, 77(4), 407–416.MathSciNetCrossRef
Zurück zum Zitat Wild, C. J., & Seber, G. A. F. (1999). Chance encounters: A first course in data analysis and inference. New York: Wiley.MATH Wild, C. J., & Seber, G. A. F. (1999). Chance encounters: A first course in data analysis and inference. New York: Wiley.MATH
Metadaten
Titel
Graphical Diagnostics, Tests, and Model Selection
verfasst von
Marius Hofert
Ivan Kojadinovic
Martin Mächler
Jun Yan
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-89635-9_5