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As mentioned here Is a covariance matrix composed of matrixes derived from separate samples guaranteed to be positive definitive? and here Must a matrix of sample pairwise covariances be PSD? if you set up a covariance matrix by plugging in pairwise covariances, then it is not guaranteed to be PSD (positive semi-definite). My questions are:

  1. Is it also the case if you don`t have NaN values ?
  2. What is the mathematical reason why covariance matrix becomes non-PSD if estimated pairwise ?

Thank you

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