Vector-valued Estimates
The above generalizes easily to the case of taking the mean of vector-valued estimates. For example, estimates of position on a plane may have less certainty in one direction than another. As in the scalar case, the weighted mean of multiple estimates can provide a maximum likelihood estimate. We simply replace by the covariance matrix:
The weighted mean in this case is:
and the covariance of the weighted mean is:
For example, consider the weighted mean of the point with high variance in the second component and with high variance in the first component. Then
then the weighted mean is:
which makes sense: the estimate is "compliant" in the second component and the estimate is compliant in the first component, so the weighted mean is nearly .
Read more about this topic: Weighted Mean
Famous quotes containing the word estimates:
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