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I have data series and I want to calculate Gini coefficients for each row as an estimate of matrix sparsity.

Hoever values contained in the rows are not exact and have error bounds.

My question is how I could incorporate those error bounds in the Ginin index computation to get not only an estimate but also the confidence intervals?

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  • $\begingroup$ Do you know how the error bounds were calculated? $\endgroup$ – Eric Farng Apr 27 '15 at 10:44
  • $\begingroup$ SD estimator with one degree of freedom on replicates, set to 95% confidence interval for a Gaussian. $\endgroup$ – Andrei Kucharavy Apr 27 '15 at 11:39
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Have you considered a Monte Carlo simulation or Bootstrap?

For Monte Carlo, simulate a random number for each value, using the distribution of your error bounds (or any distribution you feel appropriate) and then compute your Gini index. Repeat many times and get a distribution of the estimated Gini index. To create a confidence interval, consider using 1.96 * SE intervals. Also consider taking 2.5% and 97.5% percentiles.

For Bootstrap, it sounds like each value has a bunch of data behind it. So for each value, sample with replacement from the value's data to create a new sample with the same size as the original. Recompute each value using their own new sample and then compute the Gini index. Repeat the entire process many times to create a distribution of the estimated Gini index. There are many ways to create a Bootstrap confidence interval, but taking 2.5% and 97.5% percentiles is easy and common.

If you try both methods, I'd be curious how they compare.

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