A Primer on Copulas for Count Data

The authors review various facts about copulas linking discrete distributions. They show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case. They highlight some of the dangers and limitations of an undiscriminating transposition of modeling and inference practices from the continuous setting into the discrete one.

[1]  M. Kendall.  The treatment of ties in ranking problems. , 1945, Biometrika.

[2]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[3]  E. Lehmann.  Some Concepts of Dependence , 1966 .

[4]  Takemi Yanagimoto,et al.  Partial orderings of permutations and monotonicity of a rank correlation statistic , 1969 .

[5]  J. D. Esary,et al.  Relationships Among Some Concepts of Bivariate Dependence , 1972 .

[6]  B. Schweizer,et al.  Operations on distribution functions not derivable from operations on random variables , 1974 .

[7]  A. Tchen.  Inequalities for distributions with given marginals , 1976 .

[8]  W. Whitt.  Bivariate Distributions with Given Marginals , 1976 .

[9]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[10]  D. Oakes.  A Model for Association in Bivariate Survival Data , 1982 .

[11]  Marco Scarsini,et al.  On measures of concordance , 1984 .

[12]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[13]  G. Kimeldorf,et al.  Positive dependence orderings , 1987 .

[14]  R. Nelsen.  Discrete bivariate distributions with given marginals and correlation , 1987 .

[15]  Christian Genest,et al.  Concepts de dépendance et ordres stochastiques pour des lois bidimensionnelles , 1990 .

[16]  H. Joe,et al.  Further developments on some dependence orderings for continuous bivariate distributions , 1992, Annals of the Institute of Statistical Mathematics.

[17]  Piotr Mikusiński,et al.  Shuffles of Min. , 1992 .

[18]  Harry Joe,et al.  Multivariate dependence measures and data analysis , 1993 .

[19]  S. G. Meester,et al.  A parametric model for cluster correlated categorical data. , 1994, Biometrics.

[20]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[21]  T. Louis,et al.  Inferences on the association parameter in copula models for bivariate survival data. , 1995, Biometrics.

[22]  Albert W. Marshall,et al.  Copulas, marginals, and joint distributions , 1996 .

[23]  Emiliano A. Valdez,et al.  Understanding Relationships Using Copulas , 1998 .

[24]  Satishs Iyengar,et al.  Multivariate Models and Dependence Concepts , 1998 .

[25]  L. Tiret,et al.  A parametric copula model for analysis of familial binary data. , 1999, American journal of human genetics.

[26]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[27]  Jean Averous,et al.  LTD and RTI dependence orderings , 2000 .

[28]  Copules archimédiennes et tableaux de contingence à variables qualitatives ordinales , 2000 .

[29]  M. Niewiadomska-Bugaj,et al.  An algorithm for maximizing Kendall's τ , 2001 .

[30]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[31]  Holly Carley,et al.  MAXIMUM AND MINIMUM EXTENSIONS OF FINITE SUBCOPULAS , 2002 .

[32]  Philippe Lambert,et al.  Improved rank-based dependence measures for categorical data , 2003 .

[33]  C. Genest,et al.  Compound Poisson approximations for individual models with dependent risks , 2003 .

[34]  David M. Zimmer,et al.  Modelling the Differences in Counted Outcomes Using Bivariate Copula Models with Application to Mismeasured Counts , 2004 .

[35]  Dietmar Pfeifer,et al.  Modeling and Generating Dependent Risk Processes for IRM and DFA , 2004, ASTIN Bulletin.

[36]  B. Rémillard,et al.  Test of independence and randomness based on the empirical copula process , 2004 .

[37]  H. Joe.  Asymptotic efficiency of the two-stage estimation method for copula-based models , 2005 .

[38]  Mhamed Mesfioui,et al.  On the properties of some nonparametric concordance measures in the discrete case , 2005 .

[39]  Michel Denuit,et al.  Constraints on concordance measures in bivariate discrete data , 2005 .

[40]  B. Rémillard,et al.  Goodness-of-fit tests for copulas: A review and a power study , 2006 .

[41]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[42]  Susan A. Murphy,et al.  Monographs on statistics and applied probability , 1990 .

[43]  C. Genest,et al.  Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask , 2007 .

[44]  Gunky Kim,et al.  Comparison of semiparametric and parametric methods for estimating copulas , 2007, Comput. Stat. Data Anal..

[45]  Johanna Nešlehová,et al.  On rank correlation measures for non-continuous random variables , 2007 .