Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fréchet-Hoeffding upper bound

Stochastic dominance and statistical preference are stochastic orders with different interpretations: the former is based on the comparison of the marginal distributions while the latter is based on the joint distribution. Sklar's Theorem allows expressing the joint distribution in terms of the marginals by means of a copula. This paper investigates the relationship between these two stochastic orders for comonotone random variables and random variables coupled by an Archimedean copula.

[1]  B. De Baets,et al.  On the transitivity of the comonotonic and countermonotonic comparison of random variables , 2007 .

[2]  R. Nelsen.  An Introduction to Copulas , 1998 .

[3]  M. A. Arcones,et al.  Nonparametric Estimation of a Distribution Subject to a Stochastic Precedence Constraint , 2002 .

[4]  Maxim Finkelstein.  On stochastic comparisons of population age structures and life expectancies , 2005 .

[5]  R. Szekli.  Stochastic Ordering and Dependence in Applied Probability , 1995 .

[6]  Holger Dette,et al.  A test for Archimedeanity in bivariate copula models , 2011, J. Multivar. Anal..

[7]  Moshe Shaked,et al.  Stochastic orders and their applications , 1994 .

[8]  Bernard De Baets,et al.  A Fuzzy Approach to Stochastic Dominance of Random Variables , 2003, IFSA.

[9]  K. Joag-dev,et al.  Bivariate Dependence Properties of Order Statistics , 1996 .

[10]  J. Bezdek,et al.  A fuzzy relation space for group decision theory , 1978 .

[11]  Xiaohu Li,et al.  Some new stochastic comparisons for redundancy allocations in series and parallel systems , 2008 .

[12]  Bernard De Baets,et al.  On the cycle-transitive comparison of artificially coupled random variables , 2008, Int. J. Approx. Reason..

[13]  Susana Montes,et al.  Interpretation of Statistical Preference in Terms of Location Parameters , 2015, INFOR Inf. Syst. Oper. Res..

[14]  Po-Lung Yu,et al.  Probability dominance in random outcomes , 1982 .

[15]  D. Bunn.  Stochastic Dominance , 1979 .

[16]  B. De Baets,et al.  Cycle-transitive comparison of independent random variables , 2005 .

[17]  G. Choquet.  Theory of capacities , 1954 .

[18]  Didier Dubois,et al.  Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach , 2003, Artif. Intell..

[19]  Taizhong Hu,et al.  Negative dependence in the balls and bins experiment with applications to order statistics , 2006 .

[20]  Susana Montes,et al.  Statistical Preference as a Tool in Consensus Processes , 2011, Consensual Processes.

[21]  B. De Baets,et al.  On the Cycle-Transitivity of the Dice Model , 2003 .

[22]  B. De Baets,et al.  Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity , 2005, Fuzzy Sets Syst..

[24]  Susana Montes,et al.  A study on the transitivity of probabilistic and fuzzy relations , 2011, Fuzzy Sets Syst..

[25]  H. Levy,et al.  Testing for risk aversion: a stochastic dominance approach , 2001 .

[26]  Maxim Finkelstein,et al.  On stochastic comparisons of population densities and life expectancies. , 2005 .

[27]  Harshinder Singh,et al.  The stochastic precedence ordering with applications in sampling and testing , 2004, Journal of Applied Probability.

[28]  Fabio Spizzichino,et al.  Stochastic comparisons of multivariate mixture models , 2009, J. Multivar. Anal..

[29]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[30]  C. Genest,et al.  The Joy of Copulas: Bivariate Distributions with Uniform Marginals , 1986 .