Least Squares Optimal Scalingof Partially Observed Linear Systems

JAN DE LEEUW

Abstract
We study linear systems in which both the coefficients ofthe linear combinations and the variables which are combined linearlyare only partially known. This includes the two logical extremes com-pletely known and completely unknown. The systems we study includethe usual linear systems of simultaneous equations, as well as nonlin-ear multivariate analysis systems. Throughout, we use unweighted leastsquares loss functions and majorization algorithms to minimize them.We incorporate both errors-in-equations and errors-in-variables as ad-ditional unknowns into the loss function, and arrive at algorithms fordecompositions of partially unknown matrices.

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