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

Mixed Hodge structure on local cohomology with support in determinantal varieties

We employ the inductive structure of determinantal varieties to calculate the weight filtration on local cohomology modules with determinantal support. We show that the weight of a simple composition factor is uniquely determined by its support and cohomological degree. As a consequence, we obtain the equivariant structure of the Hodge filtration on each local cohomology module, and we provide a formula for its generation level. In the case of square matrices, we express the Hodge filtration in terms of the Hodge ideals for the determinant hypersurface. As an application, we describe a recipe for calculating the mixed Hodge module structure on any iteration of local cohomology functors with determinantal support.Comment: 17 pages, comments welcom

Interspecific Variation In Morphology And Swimming Performance Within Surfperches (Embiotocidae) From California

Surfperches are marine fishes that occupy nearshore habitats along the California coast. Morphology was analyzed to determine if there were differences among 19 preserved species. Principal components analysis (PCA) was used to reduce the dimensionality of the data. Morphological differences occurred among the 19 species. ANOVA revealed a habitat effect on PC2, which described the angle of attachment of the pectoral fin. Pearson correlation revealed that genetic relatedness decreased with increasing morphological differences on PC1, which described aspect ratio and body ratio. Based on PC2, four species were selected to conduct experiments on their swimming performance. Ucrit and fin beat frequency were measured in a flume to assess speed; flexibility was assessed via the body bending coefficient and the C-start escape response. Species differences were observed in all swimming performance variables, yet there were no tradeoffs in swimming fast versus maneuverability. Morphology seems to describe only part of the story