Reversing the Stein Effect

The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed data will not be protected by the minimax property of shrinkage estimators such as that of James and Stein, but instead will likely incur a greater error than if shrinkage were not used.Comment: Published in at http://dx.doi.org/10.1214/09-STS278 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A characterization of matrix groups that act transitively on the cone of positive definite matrices

AbstractIt is well known that the group of all nonsingular lower block-triangular p×p matrices acts transitively on the cone P∗ of all positive definite p×p matrices. This result has been applied to obtain several major results in multivariate statistical distribution theory and decision theory. Here a converse is established: if a matrix group acts transitively on P∗, then its group algebra must be (similar to) the algebra of all lower block-triangular p×p matrices with respect to a fixed partitioning. This implies the nonexistence of multivariate normal linear statistical models with unrestricted covariance structure that admit a transitive group action, other than those classical models invariant under a Full block-triangular group

Squaring the Circle and Cubing the Sphere: Circular and Spherical Copulas

Do there exist circular and spherical copulas in $R^d$? That is, do there exist circularly symmetric distributions on the unit disk in $R^2$ and spherically symmetric distributions on the unit ball in $R^d$, $d\ge3$, whose one-dimensional marginal distributions are uniform? The answer is yes for $d=2$ and 3, where the circular and spherical copulas are unique and can be determined explicitly, but no for $d\ge4$. A one-parameter family of elliptical bivariate copulas is obtained from the unique circular copula in $R^2$ by oblique coordinate transformations. Copulas obtained by a non-linear transformation of a uniform distribution on the unit ball in $R^d$ are also described, and determined explicitly for $d=2$.Comment: 32 pages; 15 figures submitted to: Symmetr

Correction: Separation and completeness properties for AMP chain graph Markov models

Correction of table 2 on page 1757 of 'Separation and completeness properties for AMP chain graph Markov models', Annals of Statistics, volume 29 (2001)