On generalized order statistics and maximal correlation as a measure of dependence

In the first part of this review article some recent developments of maximal correlation coefficient, introduced by Gebelein (1941) [7], and its applications in various areas of statistics are discussed. The second part is devoted to find the distributions providing the maximal correlation coefficient between generalized order statistics (gos) and dual generalized order statistics (dgos), which are introduced by Kamps (1995) [8] and Burkschat et al. (2003) [4], respectively. Finally, in the third part, general theorems are presented, which give simple non-parametric criterion for the asymptotic independence between the different elements of gos, as well as dgos.