A note on the mean volume of confidence ellipsoid for the mean of multivariate normal distribution

This paper shows that more data or information is better in estimating the mean
of a multivariate normal distribution. Precisely, the mean volume of con dence
ellipsoid for the mean decrease with addition of independent observation. This
result is obvious when the variance-covariance matrix of the multivariate normal
distribution is known, but it not so straight to see the result when the variancecovariance
matrix is unknown.

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