  Observations where additive noise is present can for many models be grouped
into a compound observation matrix, adhering to the same type of model. There
are many ways the observations can be stacked, for instance vertically,
horizontally, or quadratically. An estimator for the spectrum of the underlying
model can be formulated for each stacking scenario in the case of Gaussian
noise. We compare these spectrum estimators for the different stacking
scenarios, and show that all kinds of stacking actually decreases the variance
when compared to just taking an average of the observations. We show that,
regardless of the number of observations, the variance of the estimator is
smallest when the compound observation matrix is made as square as possible.
When the number of observations grow, however, it is shown that the difference
between the estimators is marginal: Two stacking scenarios where the number of
columns and rows grow to infinity are shown to have the same variance
asymptotically, even if the asymptotic matrix aspect ratios differ. Only the
cases of vertical and horizontal stackings display different behaviour, giving
a higher variance asymptotically. Models where not all kinds of stackings are
possible are also discussed.
