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I am reading an internal paper that says:

Let $\sigma^2 V_1$ equal the variance of $\sum_{m\in M}Z_m - Z_0$ and $\sigma^2V_2$ equal the covariance of $||M||^{-1}\sum_{m\in M}Z_m - Z_0$ and $Z_m - Z_0$.

I am unfamiliar with the notation of the $V$s. Can anyone explain what this is referring to or point me in the right direction?

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The V's are used for the variance-covariance matrix e.g. in longitudinal data where there is no longer a single variance term, but instead, a matrix representing the variance and covariance between measurements.

The example you describe appears to refer to each matrix separately depending on the subscript 1 or 2, which I don't recall seeing before.

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  • $\begingroup$ That certainly helps. But what, then, is the significant of the $\sigma^2$ in the notation? I am familiar with building out covariance matrix, usually denoted $\Sigma$, with time series data. Unless the $\sigma^2$ is just effectively factored out? $\endgroup$ Apr 15, 2014 at 6:08
  • $\begingroup$ I don't have a definitive answer on this, nor the expertise... but I believe the σ2 is essentially factored out because the diagonal variances in the matrix might differ in some predictable way and the covariances in the off-diagonals may also have some pattern. That way, the matrix contains the information for the pattern only. I am not so sure this notation works for a completely unstructured matrix, which would require a different variance and covariance parameter in each cell of the matrix that might not be directly relatable to a single σ2. $\endgroup$
    – Moose
    Apr 16, 2014 at 18:05

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