Hey Jrb599.
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.
Statement 1:
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
Statement 2:
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.