A unifying theorem for linear and total linear least squares

It is shown how both linear least-squares and total linear least-squares estimation schemes are special cases of a rank one modification of the data matrix or the sample covariance matrix. For a problem with n unknowns, there exist n linear least-squares solutions while the total linear least-squares solution is (generically) unique. When the signal-to-noise ratio is sufficiently high, the total least-squares solution is a nonnegative combination of the least-squares solutions.<
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