An Ordering for Positive Dependence

On the dependence structure of order statistics

“…PQD and hence imply (5) as well. One such notion that will be pursued here is that of greater monotone regression dependence, originally considered by Yanagimoto and Okamoto [22] and later extended and further investigated by Schriever [18], Cape´raa`and Genest [5], Block et al [3], as well as Fang and Joe [9]. Although this ordering, as all other dependence orderings, involves a comparison of the underlying copulas, an equivalent formulation of it will be given in Definition 1 below in terms of the original distributions of ðS 1 ; T 1 Þ and ðS 2 ; T 2 Þ: The latter will prove more convenient when time comes to compare pairs of order statistics, in Section 4.…”

“…SI N k 0 ðm 0 ; S 0 Þ3kpk 0 ; where k is either one of Pearson's, Spearman's or Kendall's coefficient. Numerous additional examples of bivariate distributions that are ordered in this fashion are given by Yanagimoto and Okamoto [22], Schriever [18], Cape´raa`and Genest [5,6], Fang and Joe [9], as well as Joe [10, Chapters 2 and 5]. The above definition coincides with theirs when the pairs ðS 1 ; T 1 Þ and ðS 2 ; T 2 Þ have the same margins, i.e., when F 1 ¼ F 2 and G 1 ¼ G 2 : When the margins are different, Definition 1 is then equivalent to that given by these authors, as applied to the underlying copulas C 1 and C 2 :…”

On Testing Against Positive Quadrant Dependence Based on Sub-Sample Order Statistics

“…Schriever [13] contained a large number of tests, available in the literature for the problem of independence. Shetty and Pandit [15][16][17] proposed distributionfree tests for this problem based on the ordering of observations in subsamples.…”

Specialization and partisanship in committee search

“…18 The proof of this result (for details, see our earlier working paper Moldovanu and Shi 2011) relies on a majorization theorem due to Marshall and Proschan (1965) that shows that an increase in α leads to a second-order stochastic decrease of the random utility Z i and, hence, to a higher variance. 19 This observation suggests a deeper mathematical connection: when conflict decreases, the members' random utilities become more associated, where "more association" is a well known measure of positive dependence among random variables, due to Schriever (1987). He proves the following example: Consider random variables (X 1 X 2 ) and let H α be the joint distribution function of the linear transform T α (X 1 X 2 ) = (αX 1 + (1 − α)X 2 (1 − α)X 1 + αX 2 ), where α ∈ [ 1 2 1].…”