Re: Variance of an index of dispersion

Ray Koopman <koopman@xxxxxx> wrote:
> Michael.Lacy.junk@xxxxxxxxxxxxx wrote:
>> [...]
>> The canonical article here is:
>> Agresti, A. and B. F. Agresti. 1977. "Statistical Analysis of
>> Qualitatitve Variation." Pp. 204-237 in _Sociological Methodology_
>> (ed. K. F. Schuessler).

> I would be reluctant to use asymptotic inferential methods such as
> those given in Agresti & Agresti (1978, not 1977) unless the sample
> size was very large. Alam & Mitra (Polarization Test for the
> Multinomial Distribution, JASA, 1981, 107-109) show how to get the
> exact distribution of Sum p[i]^2, and present data that lead them to
> conclude that it approaches its asymptotic distribution quite slowly.

This is interesting. I do know that in my own work on an
ordinal generalization for the Simpson measure, Monte Carlo
results showed that the asymtotic approach gave excellent
confidence coverage by N= 100 to 150, even for some pretty
skewed population distributions. Obviously, the nominal
Simpson measure could be quite different.

Another issue, though, is that any hypothesis test for
the Simpson Index or related measures is hampered by a
nuiscance parameter problem; at least this is true of
the asymptotic approaches. The difficulty is that
the same value of the dispersion measure can be
achieved by many different arrangements of the probability
vector for the i - 1, .., k categories.
Therefore, there is no unique probability vector to
serve as the foundation for the null distribution
of the nominal dispersion statistic.


--
=-=-=-=-=-=-=-=-=-==-=-=-=
Mike Lacy, Ft Collins CO 80523
Clean out the 'junk' to email me.
.

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