308 research outputs found
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
Squaring the Circle and Cubing the Sphere: Circular and Spherical Copulas
Do there exist circular and spherical copulas in ? That is, do there
exist circularly symmetric distributions on the unit disk in and
spherically symmetric distributions on the unit ball in , , whose
one-dimensional marginal distributions are uniform? The answer is yes for
and 3, where the circular and spherical copulas are unique and can be
determined explicitly, but no for . A one-parameter family of elliptical
bivariate copulas is obtained from the unique circular copula in by
oblique coordinate transformations. Copulas obtained by a non-linear
transformation of a uniform distribution on the unit ball in are also
described, and determined explicitly for .Comment: 32 pages; 15 figures submitted to: Symmetr
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
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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)
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