Did you try taking the expectations of the test statistic (where possible) to see if you get an un-biased estimator with the correction?- (Example E[G_hat] = G for unbiased-ness)
Hi I was looking at how to calculate the GINI coefficient and saw two different statements from two websites.
It has been shown that the sample Gini coefficients defined above need to be multiplied by n/(n-1) in order to become unbiased estimators for the population coefficients -http://mathworld.wolfram.com/GiniCoefficient.html
There does not exist a sample statistic that is in general an unbiased estimator of the population Gini coefficient, like the relative mean difference.-http://en.wikipedia.org/wiki/Gini_coefficient
My assumption is because wolfram is using Mu and not X-bar. Any thoughts/help?
Edit: The only reason I'm still iffy on this is because the relative mean difference does not have an unbiased estimator either and it is not divided by Mu.