Multivariate Archimedean copulas, d-monotone functions and ℓ1-norm symmetric distributions

Annals of Statistics - Tập 37 Số 5B - 2009
Alexander J. McNeil1, Johanna Nešlehová1
1Maxwell Institute, Edinburgh and ETH Zurich

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[1] Barbe, P., Genest, C., Ghoudi, K. and Rémillard, B. (1996). On Kendall’s process. <i>J. Multivariate Anal.</i> <b>58</b> 197–229.

[2] Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1989). <i>Regular Variation. Encyclopedia of Mathematics and its Applications</i> <b>27</b>. Cambridge Univ. Press, Cambridge.

[3] Boas, Jr., R. P. and Widder, D. V. (1940). Functions with positive differences. <i>Duke Math. J.</i> <b>7</b> 496–503.

[5] 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. <i>Biometrika</i> <b>65</b> 141–151.

[6] Easton, R. J., Tucker, D. H. and Wayment, S. G. (1967). On the existence almost everywhere of the cross partial derivatives. <i>Math. Z.</i> <b>102</b> 171–176.

[7] Fang, K.-T. and Fang, B.-Q. (1988). Some families of multivariate symmetric distributions related to exponential distribution. <i>J. Multivariate Anal.</i> <b>24</b> 109–122.

[9] Frees, E. W. and Valdez, E. A. (1997). Understanding relationships using copulas. <i>North American Actuarial J.</i> <b>2</b> 1–25.

[10] Genest, C., Ghoudi, K. and Rivest, L.-P. (1995). A semi-parametric estimation procedure of dependence parameters in multivariate families of distributions. <i>Biometrika</i> <b>82</b> 543–552.

[11] Genest, C. and MacKay, R. J. (1986a). Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. <i>Canad. J. Statist.</i> <b>14</b> 145–159.

[12] Genest, C. and MacKay, R. J. (1986b). The joy of copulas: Bivariate distributions with uniform marginals. <i>Amer. Statist.</i> <b>40</b> 280–283.

[13] Genest, C. and Nešlehová, J. (2007). A primer on copulas for discrete data. <i>Astin Bull.</i> <b>37</b> 475–515.

[14] Genest, C. and Rivest, L.-P. (1989). A characterization of Gumbel’s family of extreme value distributions. <i>Statist. Probab. Lett.</i> <b>8</b> 207–211.

[15] Genest, C. and Rivest, L.-P. (1993). Statistical inference procedures for bivariate Archimedean copulas. <i>J. Amer. Statist. Assoc.</i> <b>88</b> 1034–1043.

[19] Joe, H. (1997). <i>Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability</i> <b>73</b>. Chapman and Hall, London.

[20] Kimberling, C. H. (1974). A probabilistic interpretation of complete monotonicity. <i>Aequationes Math.</i> <b>10</b> 152–164.

[21] Klugman, S. A. and Parsa, R. (1999). Fitting bivariate loss distributions with copulas. <i>Insurance Math. Econom.</i> <b>24</b> 139–148.

[22] Ling, C.-H. (1965). Representation of associative functions. <i>Publ. Math. Debrecen</i> <b>12</b> 189–212.

[23] Marshall, A. W. and Olkin, I. (1988). Families of multivariate distributions. <i>J. Amer. Statist. Assoc.</i> <b>83</b> 834–841.

[25] Miller, A. D. and Vyborny, R. (1986). Some remarks on functions with one-sided derivatives. <i>Amer. Math. Monthly</i> <b>93</b> 471–475.

[26] Müller, A. and Scarsini, M. (2005). Archimedean copulae and positive dependence. <i>J. Multivariate Anal.</i> <b>93</b> 434–445.

[27] Nelsen, R. B. (1999). <i>An Introduction to Copulas. Lecture Notes in Statist.</i> <b>139</b>. Springer, New York.

[28] Nelsen, R. B. (2005). Some properties of Schur-constant survival models and their copulas. <i>Braz. J. Probab. Stat.</i> <b>19</b> 179–190.

[29] Oakes, D. (1989). Bivariate survival models induced by frailties. <i>J. Amer. Statist. Assoc.</i> <b>84</b> 487–493.

[30] Oakes, D. (1994). Multivariate survival distributions. <i>J. Nonparametr. Statist.</i> <b>3</b> 343–354.

[33] Roberts, A. W. and Varberg, D. E. (1973). <i>Convex Functions. Pure and Applied Mathematics</i> <b>57</b>. Academic Press, New York–London.

[35] Scarsini, M. (1984). On measures of concordance. <i>Stochastica</i> <b>8</b> 201–218.

[38] Sklar, A. (1959). Fonctions de répartition à <i>n</i> dimensions et leurs marges. <i>Publ. Inst. Statist. Univ. Paris</i> <b>8</b> 229–231.

[39] Whelan, N. (2004). Sampling from Archimedean copulas. <i>Quant. Finance</i> <b>4</b> 339–352.

[41] Williamson, R. E. (1956). Multiply monotone functions and their Laplace transforms. <i>Duke Math. J.</i> <b>23</b> 189–207.

[4] Cherubini, U., Luciano, E. and Vecchiato, W. (2004). <i>Copula Methods in Finance</i>. Wiley, Chichester.

[8] Fang, K.-T., Kotz, S. and Ng, K.-W. (1990). <i>Symmetric Multivariate and Related Distributions</i>. Chapman and Hall, London.

[16] Hewitt, E. and Stromberg, K. (1975). <i>Real and Abstract Analysis</i>. Springer, New York.

[17] Hoffmann-Jørgensen, J. (1994). <i>Probability with a View Toward Statistics</i>. II. Chapman and Hall, New York.

[18] Hopf, E. (1926). Über die Zusammenhänge zwischen gewissen höheren Differenzenquotienten reeller Funktionen einer reellen Variablen und deren Differenzierbarkeitseigenschaften. Ph.D. thesis, Univ. Berlin.

[24] McNeil, A. J. (2008). Sampling nested Archimedean copulas. <i>J. Statist. Comput. Simulation</i>. <b>78</b> 567–581.

[31] Popoviciu, T. (1933). Sur quelques propriétés des fonctions d’une ou de deux variables réelles. Ph.D. thesis, Faculté des Sciences de Paris.

[32] Popoviciu, T. (1944). <i>Les fonctions convexes</i>. Hermann, Paris.

[34] Saks, S. (1937). <i>Theory of the Integral</i>, 2nd ed. Hafner Publishing Co., New York.

[36] Schönbucher, P. (2003). <i>Credit Derivatives Pricing Models</i>. Wiley, Chichester.

[37] Schweizer, B. and Sklar, A. (1983). <i>Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics</i>. North-Holland Publishing Co., New York.

[40] Widder, D. V. (1946). <i>The Laplace Transform</i>. Princeton Univ. Press, Princeton.