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The shorted operator statistically interpreted. (English) Zbl 0744.62080
Summary: The object of this paper is to point out that the shorted positive operator [see M. G. Krejn, Mat. Sb., N. Ser. 20(62), 431-495 (1947; Zbl 0029.14103) and ibid. 21(63), 365-404 (1947; Zbl 0030.39401), and W. N. Anderson jun. and G. E. Trapp, SIAM J. Appl. Math. 28, 60-71 (1975; Zbl 0295.47032)] can be looked upon as the dispersion matrix of the BLUE of $$EY$$ when the random vector $$Y$$ is subject to a linear model.

##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 47N30 Applications of operator theory in probability theory and statistics 62G99 Nonparametric inference
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