A characterization of the normal distribution by sufficiency of the least squares estimation |
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| Authors: | W Bischoff H Cremers Prof Dr W Fieger |
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| Institution: | 1. Institut für Mathematische Statistik, Universit?t Karlsruhe, Englerstra?e, 7500, Karlsruhe 1, FRG
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| Abstract: | Summary For a linear modelY =ϑ + Z,ϑ ∈V,V ⊂ ℝ
n
a linear space, the following theorem is proved under simple conditions on the subspaceV: The projection onV (i.e. the least squares estimate forϑ) is a sufficient statistic iffZ is normally distributed. Further, this result is extended to the case of a multivariate linear model. |
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