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Archiver > GENEALOGY-DNA > 2011-02 > 1297202780


From: "Ken Nordtvedt" <>
Subject: Re: [DNA] variance quiz game
Date: Tue, 8 Feb 2011 15:06:20 -0700
References: <002701cbc7a9$8c29ef30$c2482dae@Ken1><4D517E86.3060904@gmail.com> <014001cbc7d0$b20d4450$c2482dae@Ken1><015e01cbc7d2$ebe67640$c2482dae@Ken1><4D51B0F0.6010807@gmail.com>


----- Original Message -----
From: "David Johnston" <>

> Ok. I see what you are getting at. You are talking about [[exploring ]]
> using these
> exact forms as estimators for T. I thought you were wondering about
> sufficient statistics.

[[Sufficient statistics are in fine shape, though we have only 4 markers in
stated case. There is nothing that emerges from the central limit theorem
that allows you to compare the width of the limiting gaussian of one
estimator from the limiting gaussian of a different estimator --- or
actually ratio of widths --- if we could go to more and more markers. Once
I found a few months ago that a combination of quadratic variance and
quartic variance could be a "better" estimator of G than the pure quadratic
variance, I have become intrigued about finding, if possible, the "best"
estimator that exists in principle.

I think it is a rather clean, straightforward problem. Given two haplotypes
and the standard simple rules of mutation for the markers of the haplotypes,
what is the best of all possible estimators that can be constructed for the
TMRCA of the two haplotypes? No further assumed information or restrictions
on form of estimator!!!!

Or stated in more raw terms: Given the simple rules of mutation for the n
markers, and final observed differences d(1), d(2), .......... d(n), what
function of the d(i) and mutation rates
m(i) is the "best" estimator for G? KN]]


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