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From: "Ken Nordtvedt" <>
Subject: [DNA] Fw: variance quiz game
Date: Tue, 8 Feb 2011 12:36:45 -0700


So I finally got the algebra and combinatorials done correctly, I think, and
the linear estimator is always superior in that it has a smaller sigma.

In the limit of old TMRCA (mG larger than one) the ratio of quadratic
estimator sigma to linear estimator sigma is SquareRoot of (4/3)


----- Original Message -----
From: "Ken Nordtvedt" <>
To: <>
Sent: Tuesday, February 08, 2011 12:20 PM
Subject: Re: [DNA] variance quiz game


>
> ----- Original Message -----
> From: "Sandy Paterson" <>
> To: <>
> Sent: Tuesday, February 08, 2011 12:08 PM
> Subject: Re: [DNA] variance quiz game
>
>
>> I'd say the first estimate is better simply because in the trivial (but
>> surely common) case where they match 3/4, the second estimate gives an
>> answer of zero which is clearly nonsense. [[ All estimators blow up in
>> fractional size of sigma as generations go to zero, so that limit must be
>> handled with care. But see below. ]]
>
> [[ What if the answer depends on the age (mG) of the pair? In fact, that
> is what i have found preliminarily. For young TMRCA the usual linear in
> Variance estimator has the smaller sigma for the estimation, but for old
> TMRCAs the latter quadratic in Variance estimator seems to have the
> smaller sigma for the estimator.
>
> Needless to say, I am checking the mathematics now that my driveway
> snowplowing is done for the morning. This would be very interesting, if
> true. KN ]]


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