Good point! Russell Davidson, the first part of the famous
Davidson-MacKinnon pair (although I tend to think they just agreed to
run alphabetically in most of their papers and books), spent a fair
amount of time on the bootstrap testing for Lorenz curve crossing, and
other issues in inequality/poverty measurement. If you are really
after a rigorous solution, you should check his work.
On 4/13/07, Mike Lacy <[email protected]> wrote:
In general, bootstrap approaches simulate the distribution of a
statistic under the assumption that the alternative hypothesis is
true, *not* under the assumption that the null is true, as an
hypothesis test would require. In some cases,the null and alternative
distributions have the same standard errors and the same shape, but
not in general. If you truly want a *test* for the difference of two
Gini coefficients, as opposed to checking whether a CI for the
difference contains (which is not truly an hypothesis test), I would
recommend you use -permute- rather than bootstrap, since -permute-
simulates the sampling distribution under the null assumption of
random assignment to groups.
--
Stas Kolenikov
http://stas.kolenikov.name
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