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I have fitted a 3 parameter (mean, sigma & tau) model to my data and have also computed the standard error for each of them. The statistic of interest for my data is the sum of mean and tau. My question is how do I estimate the total error for this new statistic? I know I can't simply add up the errors for mean and tau. Any help would be greatly appreciated. Thanks in advance.

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If you can't derive Cov(mu, tau) you can bootstrap the statistic of interest, i.e. mu+tau (note that the standard bootstrap may not be valid for non-iid data)

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