Journal of the American Statistical Association · 1981 · 5K citations · 0 references
Natural SciencesMathematicsOptimizationProbability TheoryStochastic ProcessesConvex AnalysisLinear ProgrammingMatrix ComputationMatrix FactorizationProbability InequalitiesStochastic OptimizationConcentration InequalitiesDirect ProductsMultivariate Stochastic DominanceRandom MatricesRandom Matrix TheorySymmetrization Inequalities
Introduction.- Doubly Stochastic Matrices.- Schur-Convex Functions.- Equivalent Conditions for Majorization.- Preservation and Generation of Majorization.- Rearrangements and Majorization.- Combinatorial Analysis.- Geometric Inequalities.- Matrix Theory.- Numerical Analysis.- Stochastic Majorizations.- Probabilistic, Statistical, and Other Applications.- Additional Statistical Applications.- Orderings Extending Majorization.- Multivariate Majorization.- Convex Functions and Some Classical Inequalities.- Stochastic Ordering.- Total Positivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.