We introduce a partial order, variance majorization, on R, which is analogous to the majorization order. A new class of monotonicity inequalities, based on variance majorization and analogous to Schur convexity, is developed.

Generalized variance is applied for determination of dispersion in a multivariate population and is a successful measure for concentration of multivariate data. In this article, we consider constructing confidence interval and testing the hypotheses about generalized variance in a multivariate normal distribution and give a computational approach. Simulation studies are performed to compare thi...

We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds excess variance are derived under mild conditions. In particular, it is shown that some restrictions imposed on class fast convergence rates can be achieved including optimal non-parametric expressive classes in non-Donsker regime additional assumptions. Our main app...

conjecture Jan Cameron ∗, Erik Christensen †, Allan M. Sinclair ‡,Roger R. Smith §,Stuart White ¶,Alan D. Wiggins ‖ ∗Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, U.S.A.,†Institute for Mathematiske Fag, University of Copenhagen, Copenhagen, Denmark.,‡School of Mathematics, University of Edinburgh, JCMB, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland.,§Departm...