On the distribution of a nonnegative difference between two -distributed second degree polynomial statistics
A method of finding bases of a matrix
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Estimability of linear parametric functions in a one-dimensional linear model
In the general linear model Ey=Xξ, the vector Cξ is estimable whenever there exists a matrix L such that ELy=Cξ. Several characterizations of estimability are presented. The haracterizations concern matrix and rank equalities based on X and XX′. Moreover, usefulness of such characterizations is discussed from a computational point of view. For new results on this subject see a paper by I. S. Alalouf and G. P. H. Styan
Estimability of linear parametric functions in a one-dimensional linear model with restrictions
The 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.
Algorithms 80-81. Calculation of projections
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