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I have two methods which are being used to estimate a specific signal. I have a ground truth measurement of this signal and these two methods are using noisy data to estimate this signal. This signal is computed using a sliding window, meaning that two consecutive estimates are not independent (the window is 30 seconds and a new estimate is made every 1 second, so the overlap in consecutive estimates is 29 seconds). So I now have two sets of estimates - one for each method. I want to determine which method is better, i.e. which one will have smaller residuals. I am using the absolute value of these residuals for the significance test, so the test has to be non-parametric (sort of a folded normal distribution).

The two sets of estimates are paired - they are measured at the same point in time, just using different methods. I have been looking at Wilcoxon signed-rank test but there is an assumption that each pair is independent from each other, which they are not in this case.

What is the best way to perform a statistical test on paired data for which each population is not independent?

Please let me know if any clarification is required. Thanks in advance!

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