We can regard Coavariance Intersection as special case of the solution of the barycenter of several probability distributions, when the distance measure is KL divergence. By changing the distance measure, one can get different barycenter of those probability distributions. One of the most important is the Wasserstein barycenter.

While the estimation consistency is guaranteed in Covariance Intersection, one is curious what properties does the Wasserstein barycenter holds. In this paper, it shows that the Wasserstein barycenter preserves estimation consistency under certain condition, not as general as Covariance Intersection does.

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