This paper studies the properties of the Cayley distributions, a new family of models for random pxp rotations. This class of distributions is related to the Cayley transform that maps a p(p-1)/2x1 vector s into SO(p), the space of pxp rotation matrices. First an expression for the uniform...

The asymptotic distribution of the Tukey median has recently been obtained by Nolan in a bivariate setting and by Bai and He in the general multivariate case. To establish their theorem, these authors made a strong symmetry hypothesis on the distribution and, in the case of Bai and He, assumed...

On the Banach space of real sequences converging to 0, it is shown that a probability measure may not possess an L1-median inside the space. This puts into better perspective previous results of existence of L1-medians obtained by Valadier and Kemperman.