47 research outputs found
On the distribution of a nonnegative difference between two -distributed second degree polynomial statistics
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A note on the matrix ordering of special C-matrices
No full textAbstractThe matrix inequality (∗) Δt − tt′ ⩽ Δr − rr′ is considered, where t and r are positive stochastic vectors, and Δt and Δr are diagonal matrices with t and r on their diagonals. Necessary and sufficient conditions are established (1) for (∗) to hold when t and r are given, and (2) for the existence of some vector r satisfying (∗) when t is given. The results have applications in various parts of statistics
On the Löwner, minus, and star partial orderings of nonnegative definite matrices and their squares
No full textEstimability of linear parametric functions in a one-dimensional linear model with restrictions
No full textArtykuÅ‚ nie zawiera streszczeniaThe problem of estimability of the vector Cξ in the general linear model Ey=Xξ is discussed. It is assumed that the vector of parameters ξ is a linear manifold Ω given by Rξ=s, where the matrix R and the vector s are known. The vector Cξ is estimable if there exist matrices L and M such that ELy+Ms=Cξ for all ξ in Ω. Using the results of a paper by the authors [62046 above], necessary and sufficient conditions for estimability are presented with short and elegant proofs
k-Idempotency of linear combinations of an idempotent matrix and a tripotent matrix that commute
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