Showing papers by "Ingram Olkin published in 1982"
TL;DR: In this paper, for two p-dimensional random vectors X and Y with dispersion matrices Σ11 and Σ22, respectively, it is shown that the covariance matrix Ψ 0 of X and y that minimizes the L 2 distance between them can be obtained.
279 citations
01 Jan 1982
TL;DR: In this article, the authors discuss the problem of estimating the true probability of a correct selection by using information provided by the sample, particularly for those problems in which a retrospective analysis rather than designing an experiment is carried out.
Abstract: Publisher Summary This chapter discusses the problem of estimating the true probability of a correct selection (PCS) by using information provided by the sample. This is particularly important for those problems in which a retrospective analysis rather than designing an experiment is to be carried out. The chapter also discusses the behavior of the integral α (δ1,…, δk–1) as a function of the configuration of the parameters. It explains the question how does the PCS behave if some of the δ-values are replaced by their average.
17 citations
TL;DR: Hadamard's inequality was shown to be true in this article, where it was shown that if p is an extended real valued convex function defined on a convex set A of n X n matrices, A,...,Ak E A and a.1...,ak are nonnegative numbers satisfying Eai = 1, then 4(4aAl + + +aikAk) < ao1(Aj) + * +OakO(Ak).
Abstract: Jensen's Inequality states that if p is an extended real valued convex function defined on a convex set A of n X n matrices, A,,... ,Ak E A and a.1... ,ak are nonnegative numbers satisfying Eai = 1, then 4(4aAl + +aikAk) < ao1.(Aj) + * +OakO(Ak). (2) Finally, a Convexity Result of Minkowski states that if H is an n X n positive semidefinite Hermitian matrix, then (with the convention log 0 = oo) log det H is concave, (3) (det H)1/n is concave. (4) (See e.g., Bellman (1970), p. 128, 132, Marcus and Minc (1964), p. 115, or Marshall and Olkin (1979), p. 475, 476.) Note that (4) implies (3) by virtue of the fact that concavity implies logconcavity. To prove Hadamard's Inequality, let
17 citations
TL;DR: In this article, the background of the Office of Management Budget Circular A-21, “Principles for Determining Costs Applicable to Grants, Contracts, and Other Agreements with Educational Institutions,” that describes the requirement for effort reporting is described.
Abstract: This paper describes the background of the Office of Management Budget Circular A-21, “Principles for Determining Costs Applicable to Grants, Contracts, and Other Agreements with Educational Institutions,” that describes the requirement for effort reporting. A sampling procedure is proposed as an alternative to 100% reporting.
1 citations