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This monograph brings jointly my paintings in mathematical statistics as i've got seen it throughout the lens of Jordan algebras. 3 technical domain names are to be noticeable: functions to random quadratic varieties (sums of squares), the research of algebraic simplifications of maxi mum probability estimation of patterned covariance matrices, and a extra extensive open mathematical exploration of the algebraic area from which i've got drawn the consequences utilized in the statistical difficulties simply pointed out.
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