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Our next goal is to construct a scoring matrix that is optimal to
estimate distances. An optimal estimator (scoring function) has
the smallest variance.
Let
*d*^{*} = *S*_{E}^{-1}(*w*/*n*) be our estimate of the distance using *w*.
To compute the expected value of *d*^{*}
and its variance, we use the Taylor expansion of
*S*_{E}^{-1}(*w*/*n*)
around *S*_{E}(*d*).
These computations were done with a computer
algebra system (Maple), they are too tedious and error prone to be
done by hand.

*Chantal Korostensky*

*1999-07-14*